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