MathDB
line AZ is perpendicular to BC

Source: IGO 2015 Intermediate P3

June 25, 2016
geometrygeometry proposed

Problem Statement

In triangle ABCABC ,M,N,KM,N,K are midpoints of sides BC,AC,ABBC,AC,AB,respectively.Construct two semicircles with diameter AB,ACAB,AC outside of triangle ABCABC.MK,MNMK,MN intersect with semicircles in X,YX,Y.The tangents to semicircles at X,YX,Y intersect at point ZZ.Prove that AZ⊥BCAZ \perp BC.(Mehdi E'tesami Fard)
Back to ProblemsView on AoPS