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Circles at a point. (Posted on 2014-09-07) Difficulty: 3 of 5

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.

See The Solution Submitted by broll    
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Solution Solution Comment 3 of 3 |

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

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