MathDB
Weird angle conditions again

Source: CAPS Match 2023 P3

June 30, 2023

Problem Statement

Given is a convex quadrilateral ABCDABCD with ∠BAD=∠BCD\angle BAD = \angle BCD and ∠ABC<∠ADC\angle ABC < \angle ADC. Point MM is the midpoint of segment ACAC. Prove that there exist points XX and YY on the segments ABAB and BCBC, respectively, such that XY⊥BD,MX=MYXY \perp BD, MX = MY and ∠XMY=∠ADC−∠ABC\angle XMY = \angle ADC - \angle ABC.
Proposed by Mykhailo Shtandenko
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