Let r denote the radius of the circle inscribed in this triangle.
To find the value of r, we use the formula for the area S of a triangle through the perimeter p of this triangle and the radius of the circle inscribed in this triangle, namely:
S = r * p / 2.
From this formula we get:
r = 2S / p.
According to the condition of the problem, the area of this triangle is 217, and its perimeter is 62.
Substituting these values into the formula r = 2S / p, we find the radius of the inscribed circle:
r = 2 * 217/62 = 434/62 = 7.
Answer: the radius of the inscribed circle is 7.
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