MathDB
Circle, prove two products are equal

Source: Pan African MO 2012 Day 1 Q1

October 14, 2012
geometry proposedgeometry

Problem Statement

ABAB is a chord (not a diameter) of a circle with centre OO. Let TT be a point on segment OBOB. The line through TT perpendicular to OBOB meets ABAB at CC and the circle at DD and EE. Denote by SS the orthogonal projection of TT onto ABAB . Prove that AS⋅BC=TE⋅TDAS \cdot BC = TE \cdot TD.
Back to ProblemsView on AoPS