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Source: India TST 2023 Day 2 P2

July 9, 2023
indiageometryTSTanant mudgal geo

Problem Statement

In triangle ABCABC, let DD be the foot of the perpendicular from AA to line BCBC. Point KK lies inside triangle ABCABC such that ∠KAB=∠KCA\angle KAB = \angle KCA and ∠KAC=∠KBA\angle KAC = \angle KBA. The line through KK perpendicular to like DKDK meets the circle with diameter BCBC at points X,YX,Y. Prove that AX⋅DY=DX⋅AYAX \cdot DY = DX \cdot AY
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