MathDB
China TST 2000 circumcircle of triangle ADE

Source: China TST 2000, problem 1

May 22, 2005
geometrycircumcircleconicsellipseangle bisectorgeometry unsolved

Problem Statement

Let ABCABC be a triangle such that AB=ACAB = AC. Let D,ED,E be points on AB,ACAB,AC respectively such that DE=ACDE = AC. Let DEDE meet the circumcircle of triangle ABCABC at point TT. Let PP be a point on ATAT. Prove that PD+PE=ATPD + PE = AT if and only if PP lies on the circumcircle of triangle ADEADE.
Back to ProblemsView on AoPS