MathDB
Innovatively formulated geometry

Source: RMM Extralist 2021 G1

September 18, 2023
RMM ShortlistgeometryAngle Chasing

Problem Statement

Let ABCDABCD be a parallelogram. A line through CC crosses the side ABAB at an interior point XX, and the line ADAD at YY. The tangents of the circle AXYAXY at XX and YY, respectively, cross at TT. Prove that the circumcircles of triangles ABDABD and TXYTXY intersect at two points, one lying on the line ATAT and the other one lying on the line CTCT.
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