MathDB
Perpendicular

Source: Chinese TST 2007 1st quiz P2

January 4, 2009
geometryincenterPythagorean Theoremgeometry proposed

Problem Statement

Let I I be the incenter of triangle ABC. ABC. Let M,N M,N be the midpoints of AB,AC, AB,AC, respectively. Points D,E D,E lie on AB,AC AB,AC respectively such that BD\equal{}CE\equal{}BC. The line perpendicular to IM IM through D D intersects the line perpendicular to IN IN through E E at P. P. Prove that AP⊥BC. AP\perp BC.
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