MathDB
2005 Geometry #10: Circle Traffic

Source:

May 16, 2013
geometrygeometric transformationreflectiondilationcircumcirclepower of a pointradical axis

Problem Statement

Let ABAB be a diameter of a semicircle Γ\Gamma. Two circles, ω1\omega_1 and ω2\omega_2, externally tangent to each other and internally tangent to Γ\Gamma, are tangent to the line ABAB at PP and QQ, respectively, and to semicircular arc ABAB at CC and DD, respectively, with AP<AQAP<AQ. Suppose FF lies on Γ\Gamma such that ∠FQB=∠CQA \angle FQB = \angle CQA and that ∠ABF=80∘ \angle ABF = 80^\circ . Find ∠PDQ \angle PDQ in degrees.
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