13

Part of 2007 Hanoi Open Mathematics Competitions

Problems(2)

locus , same area inside a triangle (2007 HOMC Junior Q13)

Source:

Let be given triangle

ABC

. Find all points

M

such that area of

\vartriangle MAB

\vartriangle MAC

geometryareasLocus

Source:

Let ABC be an acute-angle triangle with BC > CA. Let O, H and F be the circumcenter, orthocentre and the foot of its altitude CH, respectively. Suppose that the perpendicular to OF at F meet the side CA at P. Prove FHP = BAC.