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Proof in a circle

Source: Cono Sur 1993-problem 2

May 30, 2006
geometry unsolvedgeometry

Problem Statement

Consider a circle with centre OO, and 33 points on it, A,BA,B and CC, such that ∠AOB<∠BOC\angle {AOB}< \angle {BOC}. Let DD be the midpoint on the arc ACAC that contains the point BB. Consider a point KK on BCBC such that DK⊥BCDK \perp BC. Prove that AB+BK=KCAB+BK=KC.
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