BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Point O is the circumcenter of triangle ABC, and the length of AC i

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Elite Legendary Member
Posts: 3991
Joined: Fri Jul 24, 2015 2:28 am
Location: Las Vegas, USA
Thanked: 19 times
Followed by:37 members

Point O is the circumcenter of triangle ABC, and the length of AC i

by Max@Math Revolution » Tue Jan 28, 2020 12:01 am
[GMAT math practice question]

Point O is the circumcenter of triangle ABC, and the length of AC is 7. The length of the perimeter of triangle ABC is 19. What is the area of the circumscribed circle of triangle ABC?
1.28ps.png
A. 30 π
B. 32 π
C. 34 π
D. 36 π
E. 38 π
Top
Source: — Problem Solving |
User avatar
Elite Legendary Member
Posts: 3991
Joined: Fri Jul 24, 2015 2:28 am
Location: Las Vegas, USA
Thanked: 19 times
Followed by:37 members

Re: Point O is the circumcenter of triangle ABC, and the length of AC i

by Max@Math Revolution » Wed Jan 29, 2020 11:43 pm
=>

Since point O is the circumcenter of triangle ABC, OA = OB = OC is the radius of the circumscribed circle of the triangle.
Since the perimeter of the triangle ABC is 19, we have OA + OC + 7 = 19, OA + OA + 7 = 19, 2(OA) + 7 = 19, 2(OA) = 12, or the radius OA = 6.
Thus, the area of the circumscribed circle of the triangle is (62)π = 36π.

Therefore, the answer is D.
Answer: D
Top
Post new topic Post Reply
• Page 1 of 1