MathDB
HMMT Feb 2023 Team p3

Source:

February 20, 2023

Problem Statement

Let ABCDABCD be a convex quadrilateral such that ∠ABC=∠BCD=θ\angle ABC = \angle BCD = \theta for some acute angle θ\theta. Point XX lies inside the quadrilateral such that ∠XAD=∠XDA=90∘−θ\angle XAD = \angle XDA = 90^{\circ}-\theta. Prove that BX=XCBX = XC.
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