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DavidG@VeritasPrep Legendary Member
Joined
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Posted:
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Wed May 04, 2016 5:06 am
boomgoesthegmat wrote:

In the figure shown, the triangle is inscribed in the semicircle. If the length of line segment AB is 8 and the length of line segment BC is 6, what is the length of arc ABC?

A) 15pi
B) 12pi
C) 10pi
D) 7pi
E) 5pi

OA: E
An inscribed angle opposite a circle's diameter is 90 degrees, so we know that angle ABC is a right angle. Moreover, we can see that triangle ABC is a 3:4:5 triangle, which means that if segment BC = 6 and AB = 8, then segment AC = 10. If the diameter is 10, the circumference of the full circle is 10pi. Here, arc ABC constitutes half the circle, or 5pi.

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