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Incenters concyclic hence collinear

Source: The 1st India-Iran Friendly Competition Problem 2

June 12, 2024
geometryIncentresincenter

Problem Statement

Let ABCDABCD be a cyclic quadrilateral with circumcentre O1O_1. The diagonals ACAC and BDBD meet at point PP. Suppose the four incentres of triangles PAB,PBC,PCD,PDAPAB, PBC, PCD, PDA lie on a circle with centre O2O_2. Prove that P,O1,O2P, O_1, O_2 are collinear.
Proposed by Shantanu Nene
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