MathDB
Isosceles triangle

Source: 21-st Iberoamerican Mathematical Olympiad

April 16, 2007
geometrycircumcircleincentergeometry proposed

Problem Statement

In a scalene triangle ABCABC with ∠A=90∘,\angle A = 90^\circ, the tangent line at AA to its circumcircle meets line BCBC at MM and the incircle touches ACAC at SS and ABAB at R.R. The lines RSRS and BCBC intersect at N,N, while the lines AMAM and SRSR intersect at U.U. Prove that the triangle UMNUMN is isosceles.
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