1966 AMC 12 Problem 31
Attempt Problem 31 of the 1966 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1966 AMC 12 solutions, or check the answer key.
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31.
Triangle is inscribed in a circle with center A circle with center is inscribed in triangle is drawn, and extended to intersect the larger circle in Then we must have:
Answer: D
Small hint:
Line bisects so is the midpoint of arc
Big hint:
Compare angles in triangle to show
Solution:
Because is an angle bisector, the inscribed angles and are equal. Hence arcs and , and therefore chords and are equal.
Let and Then In triangle the exterior angle also equals Thus so
Therefore, the correct answer is D.