The triangle △SFA has a right angle at F. The points P and Q lie on the line SF such that the point P lies between S and F and the point F is the midpoint of the segment [PQ]. The circle k1 is th incircle of the triangle △SPA. The circle k2 lies outside the triangle △SQA and touches the segment [QA] and the lines SQ and SA.
Prove that the sum of the radii of the circles k1 and k2 equals the length of [FA]. geometryrectanglegeometry proposed