# The sides of an isosceles triangle are 26 and the base is 48. Find the radius of the circumscribed circle of this triangle.

September 14, 2021 | education

| It is known:

Triangle;

a = b = 26;

c = 48;

Find the radius of the circumscribed circle of this triangle.

1) First, we find the semiperimeter of the triangle.

p = (a + b + c) / 2;

p = (26 + 26 + 48) / 2 = (52 + 48) / 2 = 100/2 = 50;

2) The area of the triangle is found by Heron’s formula.

S = √ (p * (p – a) * (p – b) * (p – c));

S = √ (50 * (50 – 26) * (50 – 26) * (50 – 48)) = √ (50 * 24 * 24 * 2) = √ (24 * 24 * 100) = 24 * 10 = 240 ;

3) The radius of the circle is found by the formula:

r = (a * b * c) / (4 * S);

r = (26 * 26 * 48) / (4 * 240) = 32448/960 = 33.8.

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