Mathematics

Problem

Find the area of the kite formed by the centers of two orthogonal circles and their points of intersection, given the circles are

(x-1)^{2} + (y-2)^{2} = 16

and

(x-7)^{2} + (y-10)^{2} = R^{2}

. (Hint: Find

R

first using the orthogonality condition).