Three Tangent Circles

Three mutually tangent circles of radius one are surrounded by a larger circle that is simultaneously tangent to all three. What is the radius of the larger circle?


The centers A,B,C of the three mutually tangent circles form an equilateral triangle ABC with side = 2. The altitudes are also medians and angle bisectors (not all are drawn for clarity). They all intersect at point O.
Length of altitude:
Ratio of median:


Radius of larger circle

Answer: \frac{2\sqrt{3}+3}{3}


About mvtrinh

Retired high school math teacher.
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