MathDB
Czech republic,district round,2008,problem 2

Source:

February 25, 2012

Problem Statement

Two circles U,VU,V have distinct radii,tangent to each other externally at TT.A,BA,B are points on U,VU,V respectively,both distinct from TT,such that ∠ATB=90\angle ATB=90. (1)Prove that line ABAB passes through a fixed point; (2)Find the locus of the midpoint of ABAB.
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