The base of the isosceles triangle is 18 cm, and the lateral side is 15 cm. Find the radius of the inscribed

The base of the isosceles triangle is 18 cm, and the lateral side is 15 cm. Find the radius of the inscribed and circumscribed circle.

From the condition, we know that the base of the isosceles triangle is 18 cm, and the lateral side is 15 cm. Find the radius of the inscribed and circumscribed circle.

Let’s remember the formulas for calculating the radii of the circles:

Described circle: R = (abc) / 4S;

Inscribed circle:

r = S / p; where p = (a + b + c) / 2.

And to calculate the area of ​​a triangle, we use Heron’s formula:

S = √p (p – a) (p – b) (p – c).

We are looking for a semi-perimeter:

p = (15 + 15 + 18) / 2 = 24 cm.

S = √24 (24 – 15) (24 – 15) (24 – 18) = √24 * 9 * 9 * 6 = 9 * 12 = 108 cm ^ 2.

It remains to substitute the values ​​and calculate:

R = (15 * 15 * 18) / (4 * 108) = 4050/432 = 9.375 cm radius of the circumscribed circle;

r = 108/24 = 4.5 cm inscribed circle radius.