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In the figure shown, the triangle

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boomgoesthegmat Senior | Next Rank: 100 Posts Default Avatar
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In the figure shown, the triangle

Post Wed May 04, 2016 4:47 am


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

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Post Wed May 04, 2016 5:11 am
See here for another good question that tests this principle: http://www.beatthegmat.com/inscribed-triangle-semicircle-t74152.html

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Post 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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