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NMTC JUNIOR 2023 FINALS P2

Source: NMTC 2023 P2 (JUNIOR)

November 5, 2023
geometrycircumcirclenmtc

Problem Statement

PQRPQR is an acute scalene triangle. The altitude PLPL and the bisector RKRK of ∠QRP\angle QRP meet at HH (LL on QRQR and KK on PQPQ). KMKM is the altitude of triangle PKRPKR; it meets PLPL at NN. The circumcircle of △NKR\triangle NKR meets QRQR at SS other than QQ. Prove that SHKSHK is an isosceles triangle.
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