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fixed point, trapezoid (2022 Adygea Teachers' Geometry Olympiad p2)

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February 28, 2024
geometrytrapezoidfixedFixed point

Problem Statement

An arbitrary point PP is chosen on the lateral side ABAB of the trapezoid ABCDABCD. Straight lines passing through it parallel to the diagonals of the trapezoid intersect the bases at points QQ and RR. Prove that the sides QRQR of all possible triangles PQRPQR pass through a fixed point.
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