Given: ∆ABC, m∠C = 90° CB = 8, m∠B = 38º Find the area of a circumscribed circle. Find the area of the inscribed circle.

Circumscribed circle: Around 80.95

Inscribed circle: Around 3.298

Step-by-step explanation:

Since C is a right angle, when the circle is circumscribed it will be an inscribed angle with a corresponding arc length of 2*90=180 degrees. This means that AB is the diameter of the circle. Since the cosine of an angle in a right triangle is equivalent to the length of the adjacent side divided by the length of the hypotenuse:

To find the area of the circumscribed circle:

To find the area of the inscribed circle, you need the length of AC, which you can find with the Pythagorean Theorem:

The area of the triangle is:

The semiperimeter of the triangle is:

The radius of the circle is therefore

The area of the inscribed circle then is .

Hope this helps!

the answer to this question is in the pic