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Found problems: 1

2001 Bosnia and Herzegovina Team Selection Test, 4
Tags: radius , external tangent , internal tangent , geometry
In plane there are two circles with radiuses $r_1$ and $r_2$, 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 $A$ and $B$ and touches one of the circles in point $C$. Prove that $AC \cdot BC=r_1\cdot r_2$