Chứng minh ba điểm thẳng hàng hay

từ điểm A ở ngoài đường tròn (O) vẽ hai tiếp tuyến AB ,AC đến đường tròn (B,C tiếp điểm) Vẽ đ/kính CD (O). Đoạn thẳng AD cắt (O) tại E (E khác D) Vẽ OI vuông với DE tại I.
a) ABOC và ABIO nội tiếp
B) AB^2 = AE.AD
C) Tia OI cắt BC tại F. Cm : FD tiếp tuyến đường tròn (O)
D) Vẽ đường kính EH (O) CM: B,I,H thẳng hàng

Giải câu d:
Ta có:
HBBE  (tam giác ABE nội tiếp đường tròn đường kính HE)  (*)
Lại có:
ABIOC nội tiếp đường tròn đường kính AO (vì các góc ABO=ACO=AIO=90o )
=>góc BCO = góc BIF (góc ngoài bằng góc chắn cung đối diện)
Mà góc BED= góc BCD
Suy ra: góc BIF = góc BEI
Vậy ta có:
Góc BEI + góc BIE =góc BFI+góc BIE =90o (vì góc FIE =90o )
=>BIBE (**)
Từ (*) và (**) suy ra: BIBH (cùng vuông với BE ở B)
Kết luận: B, I,H thẳng hàng.

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Sen. Thom Tillis says he'll vote against Trump's national emergency

As you already know, the House will be voting on privileged resolution today that seeks to block Trump’s National Emergency. It will surely pass the House.
But the big question is what happens to the resolution when it gets to the Republican-controlled Senate. There are already some Republicans saying they’ll join Democrats to vote against Trump’s National Emergency.
Via CNN:
Sen. Thom Tillis will be among those Republican senators to vote in favor of a resolution against President Donald Trump’s declaration of a national emergency at the border, the North Carolina Republican made public Monday, increasing the chances that the resolution will be sent to the White House.
Tillis, who is up for re-election in 2020, wrote in an op-ed for The Washington Post that while he favors border security, he is concerned the President has overreached with the national emergency declaration.
“As a U.S. senator, I cannot justify providing the executive with more ways to bypass Congress,” he wrote. “As a conservative, I cannot endorse a precedent that I know future left-wing presidents will exploit to advance radical policies that will erode economic and individual freedoms.”
He’s not the only one.
Only four Republicans need join Democrats and here are two more…
Republicans control 53 seats in the chamber. If all Democrats vote for it, they will still need four Republican votes to help them stop Trump’s national emergency declaration. They have two, now that Tillis and Maine Sen. Susan Collins, who’s also up for re-election in 2020, have said they’ll join.
Other Republicans have also expressed concern about Trump’s decision to declare a national emergency as well.
Sen. Lisa Murkowski, a moderate Republican from Alaska, told a home-state TV station that she would “probably” support the proposal of disapproval.
“Not because I disagree with the President when it comes to border security, (or) certainly national security, but because I think it’s so important that there be clear lines when it comes to the separation of powers,” Murkowski told KTUU in Anchorage. “There’s going to be a great deal of debate as to whether or not the legal authority is there. I would suggest there probably is. The question is … is this over and above the authority that has been granted specifically to the Congress itself?”
Always Murkowski.
Almost always Collins (she did vote for Kavanaugh).
And now Thom Tillis, who has a hard F rating at Conservative Review, so it really isn’t terribly surprising.
Who will be number four in the Senate that sends this resolution to Trump’s desk?
We’re taking guesses in the comments.
Should there be a number four, Trump has already vowed to veto the bill. And once he does, it then becomes a serious uphill battle in the House and Senate. The House would need 53 Republicans to vote against it and the Senate only need 20.
So once the veto happens, the resolution is as good as dead.

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CHứng minh 3 điểm thẳng hàng của Anh Duy

Cho đường tròn (O;R) và một điểm M nằm ngoài đường tròn (O). Vẽ tiếp tuyến MA của đường tròn (O) với A là tiếp điểm. Vẽ dây cung AC của đuờng tròn tâm (O) vuômg góc với MO tại H
a' Chứng minh: H là trung điểm của AC 
b' Chứng minh: MC là tiếp tuyến của (O) 
c' Trên tia đối của AC lấy điểm Q. Từ Q vẽ hai tiếp tuyến QD và QE của đuờng tròn (O) với D và E là hai tiếp điểm. Chứng minh ba điểm M, E và D thẳng hàng.

Gọi I là giao điểm của ED và QO.
=>DE QO tại I   (1)
Áp dụng hệ thức lượng trong tam giác vuông OAM:
=>R2=OH.OM  (*)
Áp dụng hệ thức lượng trong tam giác vuông OEQ:
=>R2=OI.OQ (**)
Từ (*) và (**) suy ra: OH.OM = OI.OQ
Mà hai tam giác QOH, MOI có chung góc O.
Nên: QOH đồng dạng với MOI
ð Góc QHO=góc MIO=90o
ð MIQO  (2)
Từ (1) và (2) suy ra MI≡DE (cùng vuông góc với QO)
Vậy M,D,E thẳng hang.

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Cho 2 đường tròn O,O’ CẮT nhau ở A,B (O Ó thuộc mặt phẳng A,B).Kẻ các đường kính góc BOC và góc BO’C. Chứng minh C,A,D thẳng hàng, Cho OO=5,OB=4,ÓB=3 tính diện tích tam giác BCD

Cho 2 đường tròn O,O’ CẮT nhau ở A,B (O Ó thuộc mặt phẳng A,B).Kẻ các đường kính góc BOC và góc BO’C. Chứng minh C,A,D thẳng hàng, Cho OO=5,OB=4,ÓB=3 tính diện tích tam giác BCD

Ta có:
ü CAAB (vi góc CAB là góc nội tiếp chắn nữa đường tròn O)

ü DAAB(vi góc DAB là góc nội tiếp chắn nữa đường tròn O’)

Vậy hai đường thẳng CA ,DA trùng nhau (cùng vuông vối AB tại A)

=>C, A, D thẳng hàng

* Tính Diện tích tam giác BCD:

Đầu tiên ta thấy: 52=42+32

=>OO’2 = OB2 +O’B2

=> tam giác OO’B vuông tại B, cũng suy được tam giác BCD vuông tại B.

Vậy ta sẽ tính diện tích tam giác đựa vào hai cạnh góc vuông:


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I have no words. Thank you, Taylor Swift. (She came, she sang, I’m dead)[Dads out here living their best lives.]

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'If he slips, he falls. If he falls, he dies' -- Climbing 3,000 feet without ropes

(CNN)Any doubts as to whether Alex Honnold was the greatest rock climber of all time were doused when the American did something that no one thought was humanly possible.

In June 2017, the 33-year-old became the first person to climb Californian granite monolith El Capitan without any ropes -- a skill known as free soloing. 
Situated in Yosemite National Park, USA, the gargantuan rock face soars 3,200 feet into the air, standing almost 500 feet taller than the Burj Khalifa -- the world's tallest building.
There is simply no room for error. If he slips, he falls. If he falls, he dies.
"When I know what I'm doing and I'm climbing well, then it feels meditative, kind of relaxing and beautiful," Honnold told CNN Sport.
His achievement has since been immortalized in a breathtaking BAFTA-winning National Geographic documentary "Free Solo," which has been nominated for Best Documentary at this year's Oscars.

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I was just tryin to show off the fit

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Smollett, Sandmann, Lara Logan are the three horsemen of the media apocalypse.

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Amy Klobuchar allegedly mistreated staffers, sees difficulty getting team for 2020 run

Minnesota Sen. Amy Klobuchar is facing staff problems in her likely 2020 presidential run as top campaign aides withdraw their names from consideration amid her alleged mistreatment of the staff.

See also:  Amy Klobuchar apparently ate salad with a comb and then made her staffer clean it
The New York Times published a story Friday detailing the harsh, occasionally demeaning manner in which 2020 presidential candidate Amy Klobuchar has treated her staff. There are a lot of disturbing details in the report, including accounts of Klobuchar throwing items "in the direction of aides" and making employees wash her dishes, which is probably unethical and definitely shitty.

The weirdest story, though, is about a comb. In 2008, an aide allegedly forgot to bring a fork for Klobuchar's salad aboard a short flight to South Carolina. According to the Times, Klobuchar "berated" the staffer for his mistake, then proceeded to eat the salad with a comb.

Yes, a comb. For hair!

From the Times:
What happened next was typical: Ms. Klobuchar berated her aide instantly for the slip-up. What happened after that was not: She pulled a comb from her bag and began eating the salad with it, according to four people familiar with the episode.
Then she handed the comb to her staff member with a directive: Clean it.
It's natural for a tangle of questions to arise after reading news like this. Here are a few we're considering: What kind of comb did Klobuchar use to eat the salad? (A tail comb is likely because of its pointed end, but we do not know for sure.) We know she told the staffer to clean the comb after she was done eating, but did she clean the comb before she used it? What kind of salad was involved here? Was she able to spear a cherry tomato with that thing?

Reports of Klobuchar mistreating staff started to circulate earlier this month, when HuffPost and BuzzFeed News published interviews with former staffers about her conduct. Klobuchar responded to those stories as she announced her presidential bid on February 10.

"Yes, I can be tough, and yes I can push people,” she said. “I have high expectations for myself, I have high expectations for the people that work for me, but I have high expectations for this country.”

To be clear, the comb anecdote is not the most important part of the reports on Klobuchar's behavior. Her treatment of employees, particularly her parental leave policy — which technically required employees to pay back their leave compensation if they didn't stay on staff long enough afterward — is genuine cause for concern.

It's not just an issue for 2020, either. These incidents should be interpreted, as Libby Watson wrote for Splinter last week, as "a story of a shitty boss and workers who deserve better" — the viral stories and the less Tweet-able allegations both.

And for the love of god, clean your comb fork before you use it.
 During an interview with Fox News' Bret Baier last week, though, Klobuchar said she spoke with Reid, and “he doesn’t remember that and I don’t remember that either.”

But according to a Buzzfeed News report, numerous staffers said Klobuchar routinely sent late-night emails and berated subordinates over minor details and missteps. The report also said, "one aide was accidentally hit with a flying binder, according to someone who saw it happen, though the staffer said the senator did not intend to hit anyone with the binder when she threw it."

When asked about the report that she threw a binder, she did not flat-out deny it.

"I don't know, it's all anonymous. I will say that I'm proud of our staff," Klobuchar told Fox News last week. "And yes, I can be a tough boss, and push people -- that's obvious. But that's because I have high expectations of myself, I have high expectations of those who work for me, and I have a high expectation for our country. My chief of staff has worked for me for six years, my state director for seven years, my campaign manager for 14 years."

Asked specifically whether she had thrown a binder at someone, Klobuchar responded: "If you look at that story, I think you'll see it said something about me throwing a binder down -- not at somebody," Klobuchar said. "I just know that I should be judged, and I will take responsibility for, everything that happens on this campaign."

Some critics have charged that the criticism over Klobuchar's behavior is sexist, suggesting male managers often are not challenged for a tough management style.

A campaign spokeswoman told the Times: “The senator has repeatedly acknowledged that she can be tough and push people hard. But these anonymous stories — some of which are just plain ridiculous — do not overshadow the countless experiences of people on the senator’s team who she has been so proud to work with.”

Klobuchar announced earlier this month that she would join the crowded field of Democratic candidates lining up to take on President Trump in 2020.

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See the Galaxy Fold, Samsung's new foldable phone

Samsung unveiled the Galaxy Fold, a phone that opens into a tablet. See its new features and hefty pricetag.

See Also:  6 major challenges foldable phones need to overcome to prove they're not a fad

Foldable phones are really, finally, happening this year. But almost nobody should buy one until their many kinks are worked out.
Earlier this week, Samsung upstaged its own Galaxy S10 unveiling (all four of them) with another big announcement: its foldable Galaxy Fold phone. The nearly $2,000 luxury device, which transforms from a phone into a tablet when unfolded, is being touted as a taste of the future of mobile. 
But now that we're days removed from the Galaxy Fold's flashy reveal and merely days away from Mobile World Congress, where a handful of other Chinese phone-makers will show off their own foldable phones, I can't help but see red flags everywhere.
In 2017, I made a prediction that foldable phones had no chance of succeeding. At the time, I based my skepticism off of prototype foldable displays and the many dual-screen and foldable phones that failed to catch on.
The short of it was this: the technology to make foldable phones practical isn't ready yet And now, even without seeing the Galaxy Fold in person, I'm more certain than ever foldable phones are going to be a short-lived fad. 
That Samsung didn't feel confident enough to let any journalists try out the Galaxy Fold for themselves, especially when the device is launching in two months, is somewhat alarming.
The fact is, foldable phones are cool to look at and they're exciting to write about — it sure beats writing about another well-made Samsung knockoff that costs hundreds less — but there are clear engineering challenges that still need to be overcome for foldable phones to really herald in a new era of mobile. Solutions that not even Samsung has figured out yet. 
If foldable phones are ever to become mainstream, all of the following need to be solved.

1. The crease
There's no getting around the crease when you fold a screen in half. From afar, the crease running down the middle of the fully-opened display on the Galaxy Fold is hardly visible. But up close, which is how you'll be using it, you'll definitely see it. And once you do, you won't be able to unsee it. 
Every foldable display I've seen has a crease. There's no way to get around it, and I don't foresee any company solving this problem anytime soon. Just as there's a visible crease when you fold a piece of paper in half, the crease on foldable phone screens will be a constant reminder that you're essentially using a prototype.

2. The durability
With the crease comes the question of durability. Samsung was super gung-ho about the hinge on the Galaxy Fold. Don't get me wrong, it looks like the most beautiful hinge on a foldable screen so far (unlike the hideous wrinkly bend on the Royole FlexPai), but how many unfolds will it be able to endure? How durable is a display that you'll fold and unfold hundreds of times a day?

It's bad enough to have a single dead pixel on a screen on a $1,000 phone. What happens if the pixels along the crease start to die? Can any phone maker guarantee the pixels along a screen's crease will be good for years to come?

What about using a case? How does a case work on a foldable phone?

3. The software
Man, oh, man is the software for foldable phones not ready. Sure, Google has already thrown its full support for Android on foldable devices, but that doesn't mean squat. If the spectacular failure of Android tablets has taught us anything, it's that third-party developer support is extremely crucial to a form factor's success.

Getting developers to optimize their apps for a foldable phone's specific aspect ratio is going to be a tough challenge. It's hard enough that app developers already have to design their apps for a million different screen sizes and aspect ratios on Android, and now phone makers want them to do it again? Good luck with that. 
At least with regular phones, there are already established display aspect ratios everyone agrees on. Foldable devices, not so much. Take the Galaxy Fold: It has an outside display with a 21:9 aspect ratio and unfolded interior display with 4.2:3 aspect ratio. Neither of these are commonplace, and that's just for Samsung's phones.

Who even knows what aspect ratios Xiaomi's foldable phone (above) with two folds or Huawei's yet-to-be-seen device has.

How many developers will actually update their apps for tablets? I mean, it's been almost nine years, and Instagram still doesn't have a tablet app for iPad or Android tablets. What makes device makers think developers will suddenly come around to making tablet apps again?

4. The battery life
Phones just started getting big enough batteries to last almost two days and now you wanna take a step back all because you want a slightly larger, creased screen? Thanks, but no thanks. 

I'm curious to see how long the Galaxy Fold's 4,380 mAh battery will last when using the expanded interior screen. A 4,380 mAh battery may seem like a lot for a normal phone, but for a 7.3-inch screen, it sounds wimpy; Samsung's new Galaxy Tab S5e has a 10.5 inch screen, and it needs a 7,040 mAh battery. To put that into even greater perspective, Samsung's upcoming Galaxy S10 5G has a 4,500 mAh battery and it has a 6.7-inch screen.

What I'm saying is: battery life is gonna be an issue with these early foldable phones. Constantly unfolding and folding a screen is only gonna eat battery faster. 

Either we get shorter battery life with smaller cells or phone makers cram bigger batteries and make the foldable phone even thicker. Ugh.

5. The thickness
Samsung hasn't disclosed dimensions for the Galaxy Fold, but you don't need to be a rocket scientist to see it's thicc when folded up. You can easily get an idea of how thick the Fold is by looking at the USB-C port then doubling it.

A thick phone is acceptable if it means having like a massive 16,000 mAh battery that'll last up to five days on a single charge. But otherwise, why would anyone choose to put a brick in their pants? Foldable phones need to get significantly thinner before they're worth owning.

6. The price
Samsung's Galaxy Fold will cost $1,980 when it comes out on April 26.

That. Is. An. Insane. Amount. Of. Money.

And if Samsung thinks it can charge nearly $2,000 for a foldable phone, you can bet your lunch money Huawei and Oppo and Xiaomi won't be shy doing the same. Although Chinese phone makers are known for undercutting Samsung and Apple on pricing, they've not shied away from selling their own exorbitantly-priced phones under the guise of offering a luxury experience.

Samsung's set expectations with the Galaxy Fold, calling it a luxurious device that's designed for early adopters, but if it or any other device maker wants foldable phones to be the next big thing in mobile, prices will have to come down. Like way down. Foldable phones stand no chance if few people can afford them.

Breakthroughs at MWC 2019?
Just because Samsung hasn't figured out how to overcome these challenges doesn't mean another company hasn't.

At Mobile World Congress, we'll finally get a look at how other companies will tackle foldable phones. Will they succeed where Samsung hasn't?

I'd love to see a company prove me wrong and show me a foldable phone that has all of these issues covered. But it seems unlikely that'll happen at MWC this year. We'll probably see a bunch of head-turning prototypes, but that'll likely be it.

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Great snakes! This rattler was taken from a man in Jax Beach carrying it around and claiming to be an "agent of god." Police had him toss it in a squad car, and called FWC to capture it.

Well, meanwhile in Jacksonville Beach this morning.... 6, 7, or 8 feet? I'm not getting the tape measure out. Thank you to the Florida Fish and Wildlife Commission for relocating our guest.

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Andrew Napolitano says if NYT report is true, Trump may have attempted obstruction

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ĐỀ 01






NĂM HỌC 2015-2016

Môn: Toán

Khối lớp:10 -  Chương trình: Nâng cao



ĐỀ 01

Bài 1 (1 điểm).  Tìm tập xác định hàm số   

Bài 2 (3,5 điểm).

1.     Giải các bất phương trình sau

a)                                       b) 

2.     Xác định giá trị tham số  để hệ bất phương trình   vô nghiệm

Bài 3 (2 điểm).

1.     Cho biết  Tính các giá trị lượng giác còn lại của góc

2.     Rút gọn biểu thức  

Bài 4 (3 điểm).

Trong mặt phẳng toạ độ cho đường thẳng  và đường thẳng

1.     Xét vị trí tương đối của

2.     Xác định vị trí điểm  sao cho khoảng cách từ đến  bằng

3.     Lập phương trình đường tròn đi qua  và tiếp xúc hai đường thẳng

Bài 5 (0,5 điểm). Cho  là các số thực  thoả mãn :  Tìm giá trị lớn nhất, giá trị nhỏ nhất của biểu thức  

ĐỀ 02

Bài 1(2,5 điểm).  Giải các bất phương trình sau



Bài 2 (2 điểm).

1.     Tìm các giá trị của tham số  sao cho hàm số  xác định trên

2.     Giải bất phương trình   

Bài 3 (1,5 điểm).

1.     Tính

2.     Chứng minh đẳng thức sau không phụ thuộc vào

Bài 4 (3,5 điểm).

1.     Trong mặt phẳng toạ độ cho họ đường cong

Chứng tỏ rằng  họ  là họ các đường tròn. Xác định tâm và bán kính đường tròn có bán kính nhỏ nhất trong họ

2.     Trong mặt phẳng toạ độ  cho tam giác  có  đường cao  Điểm  thuộc đường thẳng

a)    Xác định toạ độ các đỉnh tam giác  Tính diện tích tam giác

b)    Xác định  phương trình đường tròn ngoại tiếp tam giác

Bài 5 (0,5 điểm). Cho  thoả mãn   

 Chứng minh rằng 

ĐỀ 03

Bài 1 (1,5 điểm). Giải bất phương trình    

Bài 2 (2,5 điểm).

1.     Giải hệ bất phương trình     

2.     Cho  hàm số  (là tham số)

a)    Xác định sao cho  với mọi

b)    Xác định  sao cho  bất phương trình vô nghiệm.

Bài 3 (2 điểm).

1.     Cho góc  thoả mãn  Tính giá trị của biểu thức

2.     Chứng minh đẳng thức   

Bài 4 (3,5 điểm). Trong mặt phẳng toạ độ  cho đường tròn  có phương trình  và điểm

1.     Chứng tỏ  nằm ngoài đường tròn. Lập phương trình tiếp tuyến với đường tròn biết tiếp tuyến đi qua điểm

2.     Lập phương trình đường tròn đối xứng đường tròn  qua đường thẳng

3.     Tính diện tích tam giác đều  nội tiếp đường tròn

4.     Lập phương trình đường thẳng đi qua điểm  và cắt đường tròn tại hai điểm phân biệt  sao cho

Bài 5 (0,5 điểm).  Tìm các giá trị  thỏa mãn bất phương trình:


ĐỀ 04

Bài 1(2,5 điểm).  Cho bất phương trình  (là tham số)

      1.    Giải bất phương trình (1) với  

      2.   Xác định  sao cho bất phương trình  nghiệm đúng với mọi

Bài 2 (2,5 điểm).

      1.    Giải bất phương trình  

      2.  Xác định sao cho hệ bất phuơng trình   có nghiệm duy nhất.

Bài 3 (1,5 điểm).

      1.   Cho tam giác  Chứng minh rằng 

      2.   Chứng minh rằng


Bài 4 (3 điểm).  Trong mặt phẳng toạ độ cho hình bình hành ,đỉnh   và  là hình chiếu của  trên

     1.   Lập phương trình các đường thẳng

     2.   Xác định toạ độ  các đỉnh 

     3.   Xác định vị trí điểm  sao cho  đạt giá trị bé nhất .

Bài 5.(0,5 điểm). Tìm giá trị nhỏ nhất của hàm số

ĐỀ 05

Bài 1 (1,5 điểm). Giải hệ bất phương trình  

Bài 2 (3 điểm).

       1.  Giải bất phương trình  

       2.  Xác định  để mọi  đều là nghiệm của bất phương trình   

Bài 3 (1,5 điểm).

       1.  Cho biết  Tính giá trị biểu thức 

       2.   Rút gọn biểu thức   

Bài 4 (3,5 điểm).  Trong mặt phẳng toạ độ cho các đường thẳng  và điểm

      1.  Xác định toạ độ điểm  sao cho  đạt giá trị bé nhất.

      2.  Viết phương trình đường thẳng  đối xứng  qua

      3.  Viết phương trình đường thẳng  cắt  tại  sao cho tam giác  vuông cân tại

      4.  Lập phương trình đường tròn  có tâm và cắt đường thẳng  tại hai điểm phân biệt  sao cho diện tích tam giác  bằng .

Bài 5 (0,5điểm). Tam giác  có đặc điểm gì nếu  (Với là 3 cạnh tam giác và  là diện tích tam giác


ĐỀ 06


Bài 1.(1,5 điểm)   Cho ,  là tham số.

1.Xác định giá trị  sao cho  đúng với mọi .

2. Xác định giá trị  sao cho phương trình  có hai nghiệm trái dấu.

Bài 2.(3 điểm)  Giải bất phương trình sau

 1.                                                              2.  .

Bài 3.(1,5điểm)

1.Cho biết . Tính giá trị biểu thức .

2.Chứng minh rằng:  vuông nếu .

Bài 4 (3,5 điểm). Trong mặt phẳng toạ độ ,cho

1. Xác định các tiêu điểm,tiêu cự ,tâm sai,toạ độ các đỉnh,độ dài các trục của .Vẽ (E).

2. Xác định vị trí điểm  biết

3. Tìm điểm  biết .

Bài 5.(0,5 điểm). Tìm giá trị tham số  sao cho bất phương trình   nghiệm đúng với mọi .




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