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Intersection of common internal tangents are collinear with P

Source: XVII Sharygin Correspondence P19

March 2, 2021
geometrytrigonometry

Problem Statement

A point PP lies inside a convex quadrilateral ABCDABCD. Common internal tangents to the incircles of triangles PABPAB and PCDPCD meet at point QQ, and common internal tangents to the incircles of PBC,PADPBC,PAD meet at point RR. Prove that P,Q,RP,Q,R are collinear.
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