prove an identity
Source: Ireland 1999
July 4, 2009
geometryangle bisectorgeometry proposed
Problem Statement
If is the altitude, the angle bisector, and the median of a triangle , prove that and are concurrent if and only if:
a^2(a\minus{}c)\equal{}(b^2\minus{}c^2)(a\plus{}c),
where are the lengths of the sides , respectively.