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The incircle of a trapezoid...

Source: Sharygin Correspondence Round 2024 P9

March 6, 2024
geometrytrapezoid

Problem Statement

Let ABCDABCD (AD∥BCAD \parallel BC) be a trapezoid circumscribed around a circle ω\omega, which touches the sides AB,BC,CD,AB, BC, CD, and ADAD at points P,Q,R,SP, Q, R, S respectively. The line passing through PP and parallel to the bases of the trapezoid meets QRQR at point XX. Prove that AB,QSAB, QS and DXDX concur.
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