Problem

Source: 2022 Switzerland IMO TST, Problem 2

Tags: tangency, collinear, quadrilateral, geometry, Switzerland TST



Let $ABCD$ be a convex quadrilateral such that the circle with diameter $AB$ is tangent to the line $CD$, and the circle with diameter $CD$ is tangent to the line $AB$. Prove that the two intersection points of these circles and the point $AC \cap BD$ are collinear.