|
|
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
13 May 2019, 01:38
Kudos
Bookmarks
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
48% (02:56) correct
52%
(03:25)
wrong
based on 21
sessions
History
Date
Time
Result
Not Attempted Yet
The diameter AB of a circle of radius 2 is extended to a point D outside the circle so that BD = 3. Point E is chosen so that ED = 5 and line ED is perpendicular to line AD. Segment AE intersects the circle at a point C between A and E. What is the area of triangle ABC?
A. 120/37
B. 140/39
C. 145/39
D. 140/37
E. 120/31
Attachment:
ab8a0aedc923c0f0d7ffd36e507de0b9ef4606a2.png [ 23.23 KiB | Viewed 9609 times ]
13 May 2019, 07:59
Kudos
Bookmarks
Because the radius is 2, the length of the diameter AB is 4. So the huge right triangle in the picture has a horizontal side of length 7, and a vertical side of length 5, and its area is 35/2.
Notice the small triangle ACB has a right angle, and also contains the angle at point A. But the huge triangle has a right angle and contains the angle at A as well. So these two triangles have two equal angles (and therefore three equal angles, because the fact that angles in a triangle sum to 180 will ensure the third angles are the same) and they are therefore similar triangles.
We can find the hypotenuse d of the huge triangle using Pythagoras:
d^2 = 5^2 + 7^2
d = √74
The hypotenuse of the small triangle is the circle's diameter, so is 4. So every side in the small triangle is 4/√74 as long as the matching side in the huge triangle, because the two triangles are similar, and since we multiply two sides together to find an area, the area of the small triangle will be (4/√74)^2 = 16/74 = 8/37 as big as the area of the big triangle. Since the big triangle's area is 35/2, the small triangle's area is
(8/37)(35/2) = 140/37
Notice the small triangle ACB has a right angle, and also contains the angle at point A. But the huge triangle has a right angle and contains the angle at A as well. So these two triangles have two equal angles (and therefore three equal angles, because the fact that angles in a triangle sum to 180 will ensure the third angles are the same) and they are therefore similar triangles.
We can find the hypotenuse d of the huge triangle using Pythagoras:
d^2 = 5^2 + 7^2
d = √74
The hypotenuse of the small triangle is the circle's diameter, so is 4. So every side in the small triangle is 4/√74 as long as the matching side in the huge triangle, because the two triangles are similar, and since we multiply two sides together to find an area, the area of the small triangle will be (4/√74)^2 = 16/74 = 8/37 as big as the area of the big triangle. Since the big triangle's area is 35/2, the small triangle's area is
(8/37)(35/2) = 140/37
General Discussion
26 Jun 2023, 17:46
Kudos
Bookmarks
Automated notice from GMAT Club BumpBot:
A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.
This post was generated automatically.
A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.
This post was generated automatically.
