MathDB
2013 Japan Mathematical Olympiad Finals Problem 4

Source:

February 11, 2013
ratioradical axisgeometrypower of a pointgeometry proposed

Problem Statement

Given an acute-angled triangle ABC, let HH be the orthocenter. A cirlcle passing through the points B, CB,\ C and a cirlcle with a diameter AHAH intersect at two distinct points X, YX,\ Y. Let DD be the foot of the perpendicular drawn from AA to line BCBC, and let KK be the foot of the perpendicular drawn from DD to line XYXY. Show that ∠BKD=∠CKD\angle{BKD}=\angle{CKD}.
Back to ProblemsView on AoPS