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Show that <MKN=90

Source: Iran Pre-Preparation Course Examination 1997, E3, P2

March 28, 2011
geometrygeometric transformationreflectiongeometry proposed

Problem Statement

Two circles O,O′O, O' meet each other at points A,BA, B. A line from AA intersects the circle OO at CC and the circle O′O' at DD (AA is between CC and DD). Let M,NM,N be the midpoints of the arcs BC,BDBC, BD, respectively (not containing AA), and let KK be the midpoint of the segment CDCD. Show that ∠KMN=90∘\angle KMN = 90^\circ.
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