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ANALYTIC GEO?

Source: 2024 KJMO P5

November 9, 2024
geometrycircumcircle

Problem Statement

ABCABC is a right triangle with ∠C\angle C the right angle. XX is some point inside ABCABC satisfying CA=AXCA=AX. Let DD be the feet of altitude from CC to ABAB, and Y(≠X)Y(\neq X) the point of intersection of DXDX and the circumcircle of ABXABX. Prove that AX=AYAX=AY.
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