perplexus.info :: Geometry : Circles at a point.

Circles at a point. (Posted on 2014-09-07)

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?

| Comment 1 of 3

Well, let the three points of intersection be x,y, and z. If Angle xPy = Angle xpz = Angle yPz = 120 degrees, then r = radius of C and P = the center of C.

Other configurations of the three circles are possible, and it is not clear whether the radius of C is always equal to r.

Posted by Steve Herman on 2014-09-07 10:57:16

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