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Externally tangent circles

Source: Finnish Mathematics Competition 2000, Final Round, Problem 1

November 14, 2011

geometrygeometric transformationhomothetygeometry unsolved

Problem Statement

Two circles are externally tangent at the point

A

. A common tangent of the circles meets one circle at the point

B

and another at the point

C

(

B \ne C)

. Line segments

BD

and

CE

are diameters of the circles. Prove that the points

D, A

and

C

are collinear.