MathDB

5

Part of 2014 Stanford Mathematics Tournament

Problems(1)

2014 SMT Geometry #5

Source:

2/9/2015
Let ABCABC be a triangle where ∠BAC=30∘\angle BAC = 30^\circ. Construct DD in △ABC\triangle ABC such that ∠ABD=∠ACD=30∘\angle ABD = \angle ACD = 30^\circ. Let the circumcircle of △ABD\triangle ABD intersect ACAC at XX. Let the circumcircle of △ACD\triangle ACD intersect ABAB at YY. Given that DB−DC=10DB - DC = 10 and BC=20BC = 20, find AX⋅AYAX \cdot AY.
geometrycircumcircletrapezoid