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Four Tangent Circles (Posted on 2003-10-20) Difficulty: 4 of 5
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: 4.1429 (7 votes)

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Question unique??? | Comment 11 of 13 |

Is this the only triangle that all 4 circles touch the tangents?

What if you erased the top 2 circles, pushed the nose of the triangle down (increasing the top angle, decreasing the 2 base angles, and making the base wider to keep the sides tangent to the 2 circles). Now take a 2" circle and put it back up in the nose until it is tangent to the 2 sides.

Could a circle be put into the hole in the middle such that it would be tangent to the three 2" circles, AND tangent to the 2 sides of the triangle?

  Posted by Jim on 2004-08-11 08:58:55
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