Around an equilateral triangle, a circle with a radius of 10 cm is described. Then a circle is inscribed in this triangle. Find the radius of this circle.
Let the side of a regular triangle be X cm, the radius of the inscribed circle is r cm, and the circumscribed circle is R cm.
Since the ABC triangle is correct, then:
R = X * √3 / 3 = 10 cm.
X = 30 / √3 = 10 * √3 cm.
r = X * √3 / 6 = 10 * √3 cm.
R / r = (X * √3 / 3) / 10 * √3 * √3 / 6 = 5 cm.
Answer: The radius of the inscribed circle is 5 cm.
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