MathDB
square inside a circle -> more tangent circles

Source: Romanian ROM TST 2004, problem 8

May 1, 2004
geometrygeometric transformationhomothetygeometry proposed

Problem Statement

Let Γ\Gamma be a circle, and let ABCDABCD be a square lying inside the circle Γ\Gamma. Let Ca\mathcal{C}_a be a circle tangent interiorly to Γ\Gamma, and also tangent to the sides ABAB and ADAD of the square, and also lying inside the opposite angle of ∠BAD\angle BAD. Let A′A' be the tangency point of the two circles. Define similarly the circles Cb\mathcal{C}_b, Cc\mathcal{C}_c, Cd\mathcal{C}_d and the points B′,C′,D′B',C',D' respectively. Prove that the lines AA′AA', BB′BB', CC′CC' and DD′DD' are concurrent.
Back to ProblemsView on AoPS