GRE Prep 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.
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
The two lines are tangent to the circle.
[#permalink]
Updated on: 08 Sep 2024, 00:14
Updated on: 08 Sep 2024, 00:14
8
1
42
Bookmarks
00:00
Question Stats:
36% (02:58) correct
63% (02:46) wrong based on 193 sessions
Hide Show timer Statistics
The two lines are tangent to the circle. If \(AC = 10\) and \(AB = 10 \sqrt{3}\), what is the area of the circle?
A) \(100 \pi\)
B) \(150 \pi\)
C) \(200 \pi\)
D) \(250 \pi\)
E) \(300 \pi\)
Show: ::
Attachment:
circle coordinate geometry.png [ 8.03 KiB | Viewed 4823 times ]
Originally posted by GreenlightTestPrep on 24 Jul 2018, 04:46.
Last edited by Carcass on 08 Sep 2024, 00:14, edited 3 times in total.
Last edited by Carcass on 08 Sep 2024, 00:14, edited 3 times in total.
Updated
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
The two lines are tangent to the circle.
[#permalink]
26 Jul 2018, 06:02
26 Jul 2018, 06:02
20
4
Bookmarks
GreenlightTestPrep wrote:
The two lines are tangent to the circle. If AC = 10 and AB = 10√3, what is the area of the circle?
A) 100π
B) 150π
C) 200π
D) 250π
E) 300π
If AC = 10, then BC = 10
Since ABC is an isosceles triangle, the following gray line will create two right triangles...
Now focus on the following blue triangle. Its measurements have a lot in common with the BASE 30-60-90 special triangle
In fact, if we take the BASE 30-60-90 special triangle and multiply all sides by 5 we see that the sides are the same as the sides of the blue triangle.
So, we can now add in the 30-degree and 60-degree angles
Now add a point for the circle's center and draw a line to the point of tangency. The two lines will create a right triangle (circle property)
We can see that the missing angle is 60 degrees
Now create the following right triangle
We already know that one side has length 5√3
Since we have a 30-60-90 special triangle, we know that the hypotenuse is twice as long as the side opposite the 30-degree angle.
So, the hypotenuse must have length 10√3
In other words, the radius has length 10√3
What is the area of the circle?
Area = πr2
= π(10√3)2
= π(10√3)(10√3)
= 300π
Answer: E
Cheers,
Brent
Show: ::
Attachment:
1.png [ 7.68 KiB | Viewed 1791 times ]
Attachment:
2.png [ 8.42 KiB | Viewed 1792 times ]
Attachment:
3.png [ 11.78 KiB | Viewed 1784 times ]
Attachment:
4.png [ 12.09 KiB | Viewed 1777 times ]
Attachment:
5.png [ 9.49 KiB | Viewed 1784 times ]
Attachment:
6.png [ 8.77 KiB | Viewed 1782 times ]
Attachment:
7.png [ 8.79 KiB | Viewed 1781 times ]
Attachment:
8.png [ 9.15 KiB | Viewed 1779 times ]
Attachment:
9.png [ 8.13 KiB | Viewed 1788 times ]
Attachment:
10.png [ 7.78 KiB | Viewed 1781 times ]
