Given any triangle ABC, construct the angle bisector of angle BAC and extend to meet the circumcircle of ABC in F. Prove that F is the midpoint of arc BC, and if a circle with F as centre and FB as radius is constructed, then the point P, the intersection of this new circle and FA, is the incentre of triangle ABC.
Triangle Circumcircle-Incentre Result
Can you prove the result?
A proof of the result is given on p. 190 of Some Adventures in Euclidean Geometry, which is available for purchase as downloadable PDF or printed book at More Info
Michael de Villiers, Dec 2009.