MathDB
all lines are parallel

Source: Sharygin Final 2024 8.1

August 2, 2024
geometrySharygin Geometry OlympiadSharygin 2024

Problem Statement

A circle ω\omega centered at OO and a point PP inside it are given. Let XX be an arbitrary point of ω\omega, the line XPXP and the circle XOPXOP meet ω\omega for a second time at points X1X_1, X2X_2 respectively. Prove that all lines X1X2X_1X_2 are parallel.
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