MathDB

20

Part of 1971 IMO Longlists

Problems(1)

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

Source:

1/1/2011
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.
geometrycircumcirclegeometry proposed