MathDB

1

Part of 2008 APMO

Problems(1)

prove that BPC<120

Source: APMO 2008 problem 1

3/22/2008
Let ABC ABC be a triangle with ∠A<60∘ \angle A < 60^\circ. Let X X and Y Y be the points on the sides AB AB and AC AC, respectively, such that CA \plus{} AX \equal{} CB \plus{} BX and BA \plus{} AY \equal{} BC \plus{} CY . Let P P be the point in the plane such that the lines PX PX and PY PY are perpendicular to AB AB and AC AC, respectively. Prove that ∠BPC<120∘ \angle BPC < 120^\circ.
geometryEulercircumcircleincentergeometric transformationreflectiontrigonometry