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

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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
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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
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