Prove that PA*BC = PB*AC = PC*AB
Source: VAIMO 2007, P3
January 3, 2009
geometry unsolvedgeometry
Problem Statement
A point in the interior of triangle satisfies
\angle BPC \minus{} \angle BAC \equal{} \angle CPA \minus{} \angle CBA \equal{} \angle APB \minus{} \angle ACB.
Prove that \bar{PA} \cdot \bar{BC} \equal{} \bar{PB} \cdot \bar{AC} \equal{} \bar{PC} \cdot \bar{AB}.