The sides of the triangle are 6 cm, 25 cm, 29 cm. Find the radii of the inscribed

univerkov | February 26, 2021 | education

The sides of the triangle are 6 cm, 25 cm, 29 cm. Find the radii of the inscribed and circumscribed circles and the height to the smaller side of the triangle.

By Heron’s theorem, we determine the area of the triangle ABC. The half-perimeter of the triangle is: p = (6 + 25 + 29) / 2 = 30 cm.

Then Saс = √30 * (30 – 6) * (30 – 25) * (30 – 29) = 3600 = √60 cm2.

Also Savs = AB * CH / 2.

CH = 2 * Savs / AB = 2 * 60/6 = 20 cm.

Determine the radius of the circumscribed circle: R = AB * BC * AC / 4 * Savs = 6 * 29 * 25/4 * 60 = 18.125 cm.

Determine the radius of the inscribed circle. R = Savs / p = 60/30 = 2 cm.

Answer: The height is 20 cm, the radii are 2 cm and 18.125 cm.

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