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OMK 2018 Sulong, Section B Problem 1

Source: OMK 2018 Sulong, Section B Problem 1

June 21, 2021
geometryProofcircle

Problem Statement

Let ABCABC be an acute triangle. Let DD be the reflection of point BB with respect to the line ACAC. Let EE be the reflection of point CC with respect to the line ABAB. Let Γ1\Gamma_1 be the circle that passes through A,BA, B, and DD. Let Γ2\Gamma_2 be the circle that passes through A,CA, C, and EE. Let PP be the intersection of Γ1\Gamma_1 and Γ2\Gamma_2 , other than AA. Let Γ\Gamma be the circle that passes through A,BA, B, and CC. Show that the center of Γ\Gamma lies on line APAP.
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