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Source: 2023 USAJMO Problem 2/USAMO Problem 1

March 23, 2023
USAMOUSAJMOUSA(J)MOgeometry

Problem Statement

In an acute triangle ABCABC, let MM be the midpoint of BC‾\overline{BC}. Let PP be the foot of the perpendicular from CC to AMAM. Suppose that the circumcircle of triangle ABPABP intersects line BCBC at two distinct points BB and QQ. Let NN be the midpoint of AQ‾\overline{AQ}. Prove that NB=NCNB=NC.
Proposed by Holden Mui
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