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angle chasing candidate, intersecting circles given, equal angles wanted

Source: Dutch IMO TST1 2011 p3

August 6, 2019
geometryequal anglesAngle Chasingcircles

Problem Statement

The circles Γ1\Gamma_1 and Γ2\Gamma_2 intersect at DD and PP. The common tangent line of the two circles closest to point DD touches Γ1\Gamma_1 in A and Γ2\Gamma_2 in BB. The line ADAD intersects Γ2\Gamma_2 for the second time in CC. Let MM be the midpoint of line segment BCBC. Prove that ∠DPM=∠BDC\angle DPM = \angle BDC.
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