olymmath

OME 1998

Spanish Mathematical Olympiad 1998.

Other problems

Problem 3

Let ABCABC be a triangle. Points DD and EE are taken on the line BCBC such that ADAD and AEAE are parallel to the respective tangents to the circumcircle at CC and BB . Prove that BECD=(ABAC)2\frac{BE}{CD}=\left(\frac{AB}{AC}\right)^2