In a triangle ABC, an angle of 90 degrees BC 4 an angle ACB of 45 degrees, find the area of the circle

In a triangle ABC, an angle of 90 degrees BC 4 an angle ACB of 45 degrees, find the area of the circle described around the triangle ABC.

Since a circle is circumscribed about a right-angled triangle, the hypotenuse of this triangle is the diameter of the circumscribed circle.

The ABC triangle is rectangular and isosceles, so its acute angle is 45, then AC ^ 2 = 2 * BC ^ 2 2 * 16.

AC = D = 2 * √4 cm.

Then R = D / 2 = √4 cm.

Determine the area of the circle.

Sp = π * R ^ 2 = π * 4 cm2.

Answer: The area of the circle is π * 4 cm2.