MathDB
Concurrence in Cyclic Quadrilateral

Source: IMO Shortlist 2023 G3

July 17, 2024
geometryhomothetyradical axisAZE IMO TSTPascal s theorem

Problem Statement

Let ABCDABCD be a cyclic quadrilateral with ∠BAD<∠ADC\angle BAD < \angle ADC. Let MM be the midpoint of the arc CDCD not containing AA. Suppose there is a point PP inside ABCDABCD such that ∠ADB=∠CPD\angle ADB = \angle CPD and ∠ADP=∠PCB\angle ADP = \angle PCB.
Prove that lines AD,PMAD, PM, and BCBC are concurrent.
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