MathDB
HMMT Feb 2023 team p7

Source:

February 20, 2023

Problem Statement

Let ABCABC be a triangle. Point DD lies on segment BCBC such that ∠BAD=∠DAC\angle BAD = \angle DAC. Point XX lies on the opposite side of line BCBC as AA and satisfies XB=XDXB=XD and ∠BXD=∠ACB\angle BXD = \angle ACB. The point YY is defined similarly. Prove that the lines XYXY and ADAD are perpendicular.
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