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Label the triangle's vertices A, B and C. The center of the circle is O. Find the midpoint of AB, and call it M.
Consider the right triangle OMB. Its hypothenuse, OB is the circle's radius. The angle OBM is 30 degrees, since it's half the size of CBM which is 60. The length of MB is 3cm.
Since the cosine of an angle is equal to the length of its adjacent leg over the length of a hypothenuse, we have:
cos(30) = (MB)/(OB)
(OB) = (MB)/cos(30)
(OB) = 3 / cos(30)
(OB) = 3.46
The diameter of the circle is then 2*(OB) or 6.92cm |
