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Bosnia and Herzegovina TST 2001 Day 2 Problem 1

Source: Bosnia and Herzegovina Team Selection Test 2001

September 19, 2018
geometryradiusexternal tangentinternal tangent

Problem Statement

In plane there are two circles with radiuses r1r_1 and r2r_2, one outside the other. There are two external common tangents on those circles and one internal common tangent. The internal one intersects external ones in points AA and BB and touches one of the circles in point CC. Prove that AC⋅BC=r1⋅r2AC \cdot BC=r_1\cdot r_2
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