Let the angle BAC = 2 * X, angle ACB = 3 * X, angle ABC = 7 * X.
Then 2 * X + 3 * X + 7 * X = 180.
12 * X = 180.
X = 180/12 = 15.
Then the smallest angle BAC = 2 * 15 = 300.
Then the radius of the circumscribed circle is:
R = BC / 2 * Sin30 = a / 2 * (1/2) = a cm.
Answer: The radius of the circumscribed circle is a cm.
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