The height CD drawn to the base AB of the isosceles trunk ABC is equal to 3 cm AB is equal to 8cm

The height CD drawn to the base AB of the isosceles trunk ABC is equal to 3 cm AB is equal to 8cm Find the radii of the inscribed and circumscribed circle.

Consider a right-angled triangle ADC, two legs are known in it:
CD = 3 cm (by condition);
AD = 1/2 * AB = 4 cm (property of the height of an isosceles triangle).
By the Pythagorean theorem, we find AC:
AC = √ (9 + 16) = √25 = 5 (cm).
The area of the triangle is:
S = 1/2 * AB * CD = 12 (cm²)
The radius of the inscribed circle is found by the formula:
r = (2 * S) / (a + b + c) = 24/18 = 1.3333333 ≈ 1.33 (cm).
The radius of the circumscribed circle is found by the formula:
R = (a * b * c) / (4 * S) = 200/48 = 4.16666666 ≈ 4.17 (cm).
Answer: the radii of the inscribed and circumscribed circles are 1.33 cm and 4.17 cm, respectively.