MathDB

2

Part of 2008 Cono Sur Olympiad

Problems(1)

Point on the interior of a triangle

Source: Cono Sur 2008 #2

11/17/2015
Let PP be a point in the interior of triangle ABCABC. Let XX, YY, and ZZ be points on sides BCBC, ACAC, and ABAB respectively, such that <PXC=<PYA=<PZB<PXC=<PYA=<PZB. Let UU, VV, and WW be points on sides BCBC, ACAC, and ABAB, respectively, or on their extensions if necessary, with XX in between BB and UU, YY in between CC and VV, and ZZ in between AA and WW, such that PU=2PXPU=2PX, PV=2PYPV=2PY, and PW=2PZPW=2PZ. If the area of triangle XYZXYZ is 11, find the area of triangle UVWUVW.
geometrycono surgeometry unsolved