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Compute AD, where AB is a diameter of (ABC)

Source: Finland 2013, Problem 3

May 2, 2013
trigonometrygeometry unsolvedgeometry

Problem Statement

The points A,B,A,B, and CC lies on the circumference of the unit circle. Furthermore, it is known that ABAB is a diameter of the circle and ∣AC∣∣CB∣=34.\frac{|AC|}{|CB|}=\frac{3}{4}. The bisector of ABCABC intersects the circumference at the point DD. Determine the length of the ADAD.
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