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?
B. 32 π
C. 34 π
D. 36 π
E. 38 π
Target Test Prep is 20% off right now!
Use code FLASH20
Available with Beat the GMAT members only code
MORE DETAILS
Point O is the circumcenter of triangle ABC, and the length of AC i
This topic has expert replies
-
Max@Math Revolution
- Elite Legendary Member
- Posts: 3991
- Joined: Fri Jul 24, 2015 2:28 am
- Location: Las Vegas, USA
- Thanked: 19 times
- Followed by:37 members
[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?
A. 30 π
B. 32 π
C. 34 π
D. 36 π
E. 38 π
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?
A. 30 π
B. 32 π
C. 34 π
D. 36 π
E. 38 π
Math Revolution
The World's Most "Complete" GMAT Math Course!
Score an excellent Q49-51 just like 70% of our students.
[Free] Full on-demand course (7 days) - 100 hours of video lessons, 490 lesson topics, and 2,000 questions.
[Course] Starting $79 for on-demand and $60 for tutoring per hour and $390 only for Live Online.
Email to : [email protected]
-
Max@Math Revolution
- Elite Legendary Member
- Posts: 3991
- Joined: Fri Jul 24, 2015 2:28 am
- Location: Las Vegas, USA
- Thanked: 19 times
- Followed by:37 members
=>
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
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
Math Revolution
The World's Most "Complete" GMAT Math Course!
Score an excellent Q49-51 just like 70% of our students.
[Free] Full on-demand course (7 days) - 100 hours of video lessons, 490 lesson topics, and 2,000 questions.
[Course] Starting $79 for on-demand and $60 for tutoring per hour and $390 only for Live Online.
Email to : [email protected]
