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The product is equal two 2 - [IMO LongList 1971]

Source:

January 1, 2011
geometrycircumcirclegeometry proposed

Problem Statement

Let MM be the circumcenter of a triangle ABC.ABC. The line through MM perpendicular to CMCM meets the lines CACA and CBCB at QQ and P,P, respectively. Prove that CP‾CM‾⋅CQ‾CM‾⋅AB‾PQ‾=2.\frac{\overline{CP}}{\overline{CM}} \cdot \frac{\overline{CQ}}{\overline{CM}}\cdot \frac{\overline{AB}}{\overline{PQ}}= 2.
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