A circle is described around a regular triangle. A circle is inscribed in the same triangle.
| July 4, 2021 | education
A circle is described around a regular triangle. A circle is inscribed in the same triangle. Find the ratio of the radii of these circles.
Let the side of a regular triangle be X m, 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 cm.
r = X * √3 / 6 cm.
R / r = (X * √3 / 3) / (X * √3 / 6) = 2.
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