MathDB
MN = MH wanted, ME //AC, MF //BD , cyclic ABCD given

Source: Mathley 2015 p2

August 18, 2020
cyclic quadrilateralparallelequal segments

Problem Statement

A quadrilateral ABCDABCD is inscribed in a circle and its two diagonals AC,BDAC,BD meet at GG. Let MM be the center of CD,E,FCD, E,F be the points on BC,ADBC, AD respectively such that ME∥ACME \parallel AC and MF∥BDMF \parallel BD. Point HH is the projection of GG onto CDCD. The circumcircle of MEFMEF meets CDCD at NN distinct from MM. Prove that MN=MHMN = MH
Tran Quang Hung, Nguyen Le Phuoc, Thanh Xuan, Hanoi
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