MathDB
product of radii, common tangents to circles (2021 Kyiv City MO Round2 11.3.1)

Source:

February 15, 2021
geometryTangentscircles

Problem Statement

Two circles k1k_1 and k2k_2 with radii r1r_1 and r2r_2 have no common points. The lineAB AB is a common internal tangent, and the line CDCD is a common external tangent to these circles, where A,C∈k1A, C \in k_1 and B,D∈k2B, D \in k_2. Knowing that AB=12AB=12 and CD=16CD =16, find the value of the product r1r2r_1r_2.
Back to ProblemsView on AoPS