The sides of the triangle are 14cm 16cm 18cm. Find the radius of the circumscribed circle.
| May 19, 2021 | education
Knowing the lengths of the sides of the triangle, by Heron’s theorem, we determine the area of the triangle ABC
The perimeter of the ABC triangle is: Rasv = 14 + 16 + 18 = 48 cm, then the half-perimeter p = 48/2 = 24 cm.
Savs = √p * (p – AB) * (p – BC) * (p – AC) = √24 * 8 * 10 * 6 = √11520 = 48 * √5 cm2.
Determine the radius of the circumscribed circle.
R = AB * BC * AC / 4 * S = 16 * 14 * 18/4 * 48 * √5 = 42 / √5 = 42 * √5 / 5 = 8.4 * √5 cm.
Answer: The radius of the circumscribed circle is 8.4 * √5 cm.
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