Let there be given three circles K1,K2,K3 with centers O1,O2,O3 respectively, which meet at a common point P. Also, let K1∩K2={P,A},K2∩K3={P,B},K3∩K1={P,C}. Given an arbitrary point X on K1, join X to A to meet K2 again in Y , and join X to C to meet K3 again in Z.
(a) Show that the points Z,B,Y are collinear.
(b) Show that the area of triangle XYZ is less than or equal to 4 times the area of triangle O1O2O3. geometrycircumcirclegeometry unsolved