MathDB
Iran(3rd round)2009

Source: Problem 5 Geometry

September 13, 2009
geometry unsolvedgeometry

Problem Statement

5-Two circles S1 S_1 and S2 S_2 with equal radius and intersecting at two points are given in the plane.A line l l intersects S1 S_1 at B,D B,D and S2 S_2 at A,C A,C(the order of the points on the line are as follows:A,B,C,D A,B,C,D).Two circles W1 W_1 and W2 W_2 are drawn such that both of them are tangent externally at S1 S_1 and internally at S2 S_2 and also tangent to l l at both sides.Suppose W1 W_1 and W2 W_2 are tangent.Then PROVE AB \equal{} CD.
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