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Geometry

Source: 1997 National High School Mathematics League, Exam Two, Problem 1

March 4, 2020
geometry

Problem Statement

Two circles with different radius O1O_1 and O2O_2 are both tangent to a larger circle OO, tangent points are S,TS,T. Note that intersections of O1O_1 and O2O_2 are M,NM,N, prove that the sufficient and necessary condition of OM⊥MNOM\perp MN is S,N,TS,N,T are colinear.
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