# The height of a regular triangle is 90. Find the radius of the circle circumscribed about this triangle.

January 26, 2021 | education

| First way.

In a regular triangle, the point of intersection of heights is the center of the inscribed and circumscribed circles and are divided at this point in the ratio of 2/1, starting from the vertex.

Then ВO / HO = 2/1.

OH = BO / 2.

OH + ВO = ВН = 90 cm.

ВO / 2 + ВO = 90.

3 * ВO / 2 = 90.

ВO = R = 90 * 2/3 = 60 cm.

Second way. In a regular triangle, the height is: h = a * √3 / 2, where a is the side of the triangle. Then a = 2 * h / √3 = 2 * 90 / √3 = 180 / √3 cm.

The radius of the circumscribed circle around a regular triangle is: R = a / √3 = 180 / √3 * √3 = 60 cm.

Answer: The radius of the circumscribed circle is 60 cm.

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