MathDB
Equal Angles

Source: 2003 China Second Round Olympiad

August 30, 2014
trigonometrygeometry unsolvedgeometry

Problem Statement

From point PP outside a circle draw two tangents to the circle touching at AA and BB. Draw a secant line intersecting the circle at points CC and DD, with CC between PP and DD. Choose point QQ on the chord CDCD such that ∠DAQ=∠PBC\angle DAQ=\angle PBC. Prove that ∠DBQ=∠PAC\angle DBQ=\angle PAC.
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