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Proving lengths are equal

Source: Malaysian SST 2024 P1

September 5, 2024
geometry

Problem Statement

A cyclic quadrilateral ABCDABCD has diameter ACAC with circumcircle ω\omega. Let KK be the foot of the perpendicular from CC to BDBD, and the tangent to ω\omega at AA meets BDBD at TT. Let the line AKAK meets ω\omega at XX and choose a point YY on line AKAK such that ∠TYA=90∘\angle TYA=90^{\circ}. Prove that AY=KXAY=KX.
Proposed by Anzo Teh Zhao Yang
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