perplexus.info :: Shapes : Four Tangent Circles

Four Tangent Circles (Posted on 2003-10-20)

Four circles are tangent to each other and to a triangle that surrounds them, as shown in the figure. Each of the three circles in the corners have a radius of 1 cm. What is the radius of the circle in the middle?

No Solution Yet Submitted by Bryan

Rating: 4.2500 (8 votes)

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Exterior Angle

| Comment 12 of 13 |

Using SilverKnight's notation.

sin(<BAF) = BF/BA = (R-1)/(R+1)

cos(<BAF) = FA/BA = 2*√R/(R+1)

sin(<DBC) = DC/DB = 1/(R+1)

sin(<DBC) = sin(2*<BAF) = 2*sin(BAF)*cos(<BAF)

Combining these equations give Brian Smith's cubic.

Posted by Bractals on 2004-08-12 02:06:55

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