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Reflection of Perpendicular Bisector

Source: BdMO 2023 Higher Secondary National P7

February 12, 2023
geometryreflectionpower of a pointperpendicular bisector

Problem Statement

Let ΔABC\Delta ABC be an acute triangle and ω\omega be its circumcircle. Perpendicular from AA to BCBC intersects BCBC at DD and ω\omega at KK. Circle through AA, DD and tangent to BCBC at DD intersect ω\omega at EE. AEAE intersects BCBC at TT. TKTK intersects ω\omega at SS. Assume, SDSD intersects ω\omega at XX. Prove that XX is the reflection of AA with respect to the perpendicular bisector of BCBC.
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