The sides of an isosceles triangle are 625 and the base is 350. Find the radius of the inscribed circle.

Find the radius of the circumscribed circle of this triangle.

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

p = (a + b + c) / 2 = (625 + 625 + 350) / 2 = (1250 + 350) / 2 = 1600/2 = 800;

2) Find the area of the triangle using Heron’s formula.

S = √ (p * (p – a) * (p – b) * (p – c)) = √ (800 * (800 – 625) * (800 – 625) * (800 – 350) = √ (800 * 175 * 175 * 450) = 175 * √ (800 * 450) = 175 * 10 * √ (8 * 450) = 175 * 10 * 60 = 175 * 600 = 105000;

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

r = (a * b * c) / (4 * S) = (625 * 625 * 350) / (4 * 105000) = 325.5.