MathDB
Prove that PQ=2HP

Source: LXII Polish Olympiad 2011, Problem 5

April 20, 2011
geometry3D geometrytetrahedroncircumcirclegeometry proposed

Problem Statement

In a tetrahedron ABCDABCD, the four altitudes are concurrent at HH. The line DHDH intersects the plane ABCABC at PP and the circumsphere of ABCDABCD at Q≠DQ\neq D. Prove that PQ=2HPPQ=2HP.
Back to ProblemsView on AoPS