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Incenter and intersection of lines making rhombus

Source: Azerbaijan NMO 2023. Junior P2

August 24, 2023
geometryAZE JUNIOR NATIONAL MO

Problem Statement

Let II be the incenter in the acute triangle ABC.ABC. Rays BIBI and CICI intersect the circumcircle of triangle ABCABC at points SS and T,T, respectively. The segment STST intersects the sides ABAB and ACAC at points KK and L,L, respectively. Prove that AKILAKIL is a rhombus.
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