MathDB
2012-2013 Winter OMO #38

Source:

January 16, 2013
Online Math Opengeometrycircumcirclegeometric transformationrotationparallelogramLaTeX

Problem Statement

Triangle ABCABC has sides AB=25AB = 25, BC=30BC = 30, and CA=20CA=20. Let P,QP,Q be the points on segments AB,ACAB,AC, respectively, such that AP=5AP=5 and AQ=4AQ=4. Suppose lines BQBQ and CPCP intersect at RR and the circumcircles of △BPR\triangle{BPR} and △CQR\triangle{CQR} intersect at a second point S≠RS\ne R. If the length of segment SASA can be expressed in the form mn\frac{m}{\sqrt{n}} for positive integers m,nm,n, where nn is not divisible by the square of any prime, find m+nm+n.
Victor Wang
Back to ProblemsView on AoPS