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# Kissing Circles

## Question

If three circles are mutually tangent where one has a radius of 3cm, another has a radius of 4cm, and the last has a radius of 5cm. What is the area of the region bounded between the three circles?

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triangle 7,8,9 w/ height: 7.6665

angles: 73.39798, 58.41164, 48.19038 deg

sectors areas:5.7647, 8.1535, 10.5135

Edited by TimeSpaceLightForce
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Triangle formed by centers:
sides: 7 , 8, 9
angles:73,58,48 (using laws)
Area: 26.8328 (Heron's)
Sector areas of circles:
3cm: pi3x3x73/360=5.7334
4cm:pi4x4x58/360=8.0983
5cm:pi5x5x48/360=10.4720
Area of sectors=24.30371
Area between circles is 2.52909
area ( triangle -sectors) formed

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2.01 approx.

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Triangle formed by centers:
sides: 7 , 8, 9
angles:73,58,48 (using laws)
Area: 26.8328 (Heron's)
Sector areas of circles:
3cm: pi3x3x73/360=5.7334
4cm:pi4x4x58/360=8.0983
5cm:pi5x5x48/360=10.4720
Area of sectors=24.30371
Area between circles is 2.52909
area ( triangle -sectors) formed

My answer is most like yours but my sector areas were different (for the 4cm and 5cm circles).

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