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Show that kd bisects

Source: India National Olympiad 2003, Problem 1

October 10, 2005
trigonometrygeometryalgebrapolynomialangle bisector

Problem Statement

Let PP be an interior point of an acute-angled triangle ABCABC. The line BPBP meets the line ACAC at EE, and the line CPCP meets the line ABAB at FF. The lines APAP and EFEF intersect each other at DD. Let KK be the foot of the perpendicular from the point DD to the line BCBC. Show that the line KDKD bisects the angle ∠EKF\angle EKF.
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