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Tuymaada 2022

Source: Tuymaada 2022 Senior P-8

September 12, 2022
geometrymediansines

Problem Statement

In an acute triangle △ABC\triangle ABC the points Cm,Am,BmC_m, A_m, B_m are the midpoints of AB,BC,CAAB, BC, CA respectively. Inside the triangle △ABC\triangle ABC a point PP is chosen so that ∠PCB=∠BmBC\angle PCB = \angle B_mBC and ∠PAB=∠ABBm.\angle PAB = \angle ABB_m. A line passing through PP and perpendicular to ACAC meets the median BBmBB_m at E.E. Prove that EE lies on the circumcircle of the triangle △AmBmCm.\triangle A_mB_mC_m. (K. Ivanov )
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