The sides of an isosceles triangle are 35 base 42 find the radius of the circumscribed circle of this triangle

It is known:

Isosceles triangle;

a = b = 35;

c = 42;

Find the radius of the circumscribed circle of this triangle.

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

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

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

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

3) Find the semi-perimeter of the triangle.

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

Let’s substitute the known values in all formulas in order.

4) p = (35 + 35 + 42) / 2 = (70 + 42) / 2 = 112/2 = 56;

5) S = √ (56 * (56 – 35) * (56 – 35) * (56 – 42)) = √ (56 * 21 * 21 * 14) = √ (4 * 14 * 21 * 21 * 21 * 14) = 2 * 14 * 21 = 28 * 21 = 588;

6) r = (35 * 35 * 42) / (4 * 588) = (35 * 35 * 21) / (2 * 28 * 21) = (35 * 35) / (2 * 28) = (5 * 35 ) / (2 * 4) = 175/28 = 21.875.