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CSMO Grade 10 Problem 5

Source: CSMO Grade 10 Problem 5

August 6, 2017
geometryperpendicular

Problem Statement

Let ABCDABCD be a cyclic quadrilateral inscribed in circle OO, where AC⊥BDAC\perp BD. M,NM,N are the midpoint of arc ADC,ABCADC,ABC. DODO and ANAN intersect each other at GG, the line passes through GG and parellel to NCNC intersect CDCD at KK. Prove that AK⊥BMAK\perp BM.
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