MathDB
Cono Sur Shortlist 2012, Problem G3

Source:

August 23, 2014
geometrycircumcirclepower of a pointradical axisgeometry proposed

Problem Statement

Let ABCABC be a triangle, and MM, NN, and PP be the midpoints of ABAB, BCBC, and CACA respectively, such that MBNPMBNP is a parallelogram. Let RR and SS be the points in which the line MNMN intersects the circumcircle of ABCABC. Prove that ACAC is tangent to the circumcircle of triangle RPSRPS.
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