MathDB

4

Part of 2014 Turkey Junior National Olympiad

Problems(1)

Two equations hold then two segments have equal length

Source: Turkey Junior MO 2014 Problem 4

11/16/2014
ABCABC is an acute triangle with orthocenter HH. Points DD and EE lie on segment BCBC. Circumcircle of △BHC\triangle BHC instersects with segments ADAD,AEAE at PP and QQ, respectively. Prove that if BD2+CD2=2DP⋅DABD^2+CD^2=2DP\cdot DA and BE2+CE2=2EQ⋅EABE^2+CE^2=2EQ\cdot EA, then BP=CQBP=CQ.
geometrycircumcircletrapezoidgeometry proposed