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equal angles wanted, 4 midpoints related

Source: INAMO Shortlist 2014 G5

July 13, 2019
geometryequal anglesmidpoints

Problem Statement

Given a cyclic quadrilateral ABCDABCD. Suppose E,F,G,HE, F, G, H are respectively the midpoint of the sides AB,BC,CD,DAAB, BC, CD, DA. The line passing through GG and perpendicular on ABAB intersects the line passing through HH and perpendicular on BCBC at point KK. Prove that ∠EKF=∠ABC\angle EKF = \angle ABC.
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