15 Degree Triangle

Problem

In the diagram below, $AB$ represents the diameter, $C$ lies on the circumference of the circle, and you are given that (Area of Circle) / (Area of Triangle) = $2\pi$.

Prove that the two smaller angles in the triangle are exactly $15^o$ and $75^o$ respectively.

Problem ID: 361 (11 Oct 2009)     Difficulty: 4 Star

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