A circle of radius ρ is tangent to the sides AB and AC of the triangle ABC, and its center K is at a distance p from BC.(a) Prove that a(p−ρ)=2s(r−ρ), where r is the inradius and 2s the perimeter of ABC.
(b) Prove that if the circle intersect BC at D and E, then
DE=r1−r4rr1(ρ−r)(r1−ρ)where r1 is the exradius corresponding to the vertex A. geometryinradiusperimeterexradiusIMO ShortlistIMO Longlist