In triangle ABC, the sides are 5, 6 and 7. Find the radius of the circle circumscribed about the triangle.

We calculate the semiperimeter of the triangle ABC and, by Heron’s theorem, determine the area of the triangle.

p = (AB + BC + AC) / 2 = (6 + 5 + 7) / 2 = 9 cm.

Then Savs = √p * (p – AB) * (p – BC) * (p – AC) = √9 * (9 – 6) * (9 – 5) * (9 – 7) = √9 * 3 * 4 * 2 = √216.

Sавс = 6 * √6 cm.

Then the radius of the circumscribed circle will be equal to: R = AB * BC * AC / 4 * Savs = 6 * 5 * 7/4 * 6 * √6 = 35 * √6 / 24 cm.

Answer: The radius of the circumscribed circle is 35 * √6 / 24 cm.