Three circles of common radius, r, are drawn through a common point, P. A three-point circle, C, is drawn through their pairwise points of intersection.

Determine the radius of C.

Let Q, R, and S be the centers of the

three circles. Let Q', R', and S' be

the second intersections of circles 

R&S, S&Q, and Q&R. Let P' be the point

such that rhombi Q'RS'P', R'SQ'P', and

S'QR'P' are similar to rhombi SPQR',

QPRS', and RPSQ' respectively. Point P'

is the center of circle C and hence

its radius is also r.

Edited on September 7, 2014, 7:45 pm

Posted by Bractals on 2014-09-07 19:44:48