The centers of the inscribed and circumscribed about an equilateral triangle coincide.
| September 5, 2021 | education
The centers of the inscribed and circumscribed about an equilateral triangle coincide. Prove that the radius of the circumcircle is twice the radius of the circumcircle.
If the center of an equilateral triangle coincides with the center of the inscribed and circumscribed circle and is the point of intersection of heights and medians, then according to the third property of an equilateral triangle, the radius of the circumscribed circle will be twice as large as the radius of the inscribed circle: R = 2⋅r
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