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Part of 2006 Pan African

Problems(1)

Two equal segments defined by perpendicular diameters

Source: Pan African MO 2006 Q1

5/1/2013
Let ABAB and CDCD be two perpendicular diameters of a circle with centre OO. Consider a point MM on the diameter ABAB, different from AA and BB. The line CMCM cuts the circle again at NN. The tangent at NN to the circle and the perpendicular at MM to AMAM intersect at PP. Show that OP=CMOP = CM.
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