MathDB
Cono Sur Shortlist 2012, Problem G1

Source:

August 23, 2014
geometrycircumcirclegeometry proposed

Problem Statement

Let ABCDABCD be a cyclic quadrilateral. Let PP be the intersection of BCBC and ADAD. Line ACAC intersects the circumcircle of triangle BDPBDP in points SS and TT, with SS between AA and CC. Line BDBD intersects the circumcircle of triangle ACPACP in points UU and VV, with UU between BB and DD. Prove that PSPS = PTPT = PUPU = PVPV.
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