I saw the image of the triangle. It will be a circle inscribed in an isosceles triangle.
sides a and b have 18 cm and side c have 20 cm.
The triangle can be divided into 2 right triangles with 10 cm base, 18 cm hypotenuse. We need to find the measure of the long side to get the height of the isosceles triangle.
a² + b² = c²
a² + (10cm)² = (18cm)²
a² = 324 cm² - 100 cm²
a² = 224 cm²
a = √224 cm²
a = 14.97 cm
Area = 1/2 * base * height
A = 1/2 * 20 cm * 14.97 cm
A = 149.70 cm²
A = r/2 * p
149.70 cm² = r/2 * (18cm+18cm+20cm)
149.70 cm² = r/2 * 56 cm
149.70 cm² ÷ 56 cm = r/2
2.67 cm = r/2
2.67 cm * 2 = r
5.34 cm = r
Radius is 5.35 cm.