Problem:
Three circles of radius 1 are externally tangent to each other and internally tangent to a larger circle. What is the radius of the large circle?
Answer Choices:
A. 32+6​​
B. 2
C. 32+32​​
D. 33+23​​
E. 23+3​​
Solution:
Let O be the center of the large circle, let C be the center of one of the small circles, and let OA and OB be tangent to the small circle at A and B.
By symmetry, ∠AOB=120∘ and ∠AOC=60∘. Thus △AOC is a 30−60−90 degree right triangle, and AC=1, so
OC=3​2​AC=323​​
If OD is a radius of the large circle through C, then
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