Excenter

The excenter opposite A in triangle ABC is the intersection of the internal bisector of angle A and the external bisectors of angles B and C. This point is the center of a circle tangent to the triangle's three sides but lying outside it. Every triangle has exactly three excircles, one for each vertex. The distance from vertex A to the point where the excircle touches side AB (or side AC) equals the triangle's semiperimeter.