MathDB

5

Part of 1999 Taiwan National Olympiad

Problems(1)

$BN>CN$

Source: 8-th Taiwanese Mathematical Olympiad 1999

1/21/2007
Let AD,BE,CFAD,BE,CF be the altitudes of an acute triangle ABCABC with AB>ACAB>AC. Line EFEF meets BCBC at PP, and line through DD parallel to EFEF meets ACAC and ABAB at QQ and RR, respectively. Let NN be any poin on side BCBC such that NQP^+NRP^<1800\widehat{NQP}+\widehat{NRP}<180^{0}. Prove that BN>CNBN>CN.
geometrycircumcirclegeometry unsolved