MathDB

19

Part of 2010 Sharygin Geometry Olympiad

Problems(1)

Prove that XV=YU (19)

Source:

10/29/2010
A quadrilateral ABCDABCD is inscribed into a circle with center O.O. Points PP and QQ are opposite to CC and DD respectively. Two tangents drawn to that circle at these points meet the line ABAB in points EE and F.F. (AA is between EE and BB, BB is between AA and FF). The line EOEO meets ACAC and BCBC in points XX and YY respectively, and the line FOFO meets ADAD and BDBD in points UU and VV respectively. Prove that XV=YU.XV=YU.
geometryparallelogramcircumcirclegeometry unsolved