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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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not that dificult... | Comment 8 of 13 |
Okay maybe i'm over simplifying but here is what I did- Cut off the top of the triangle halfway between the top circle and cut the bottom off halfway between the bottom circles. Now you have a trapezoid with length 2 on top and length 4 on the bottom. The diameter of the large circle, because it is halfway between the top and bottom sides of the trapezoid must be halfway between 2 and 4 which gives us 3. Half of three is the radius or 1.5.
  Posted by karin on 2004-03-18 13:15:29
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