A circle is described about a right-angled triangle with leg A and an adjacent acute angle equal to.

A circle is described about a right-angled triangle with leg A and an adjacent acute angle equal to. What is the area of a circle?

Since the triangle inscribed in the circle is rectangular, its inscribed angle ABC = 90 and rests on the arc AC, the degree measure of which is: AC = 2 * 90 = 180.

Then the hypotenuse AC is the diameter of the circumscribed circle.

In a right-angled triangle ABC Cosα = BC / AC.

AC = BC / Cosα = a / Cosα.

Then R = AC / 2 = a / 2 * Cosα.

Determine the area of the circle.

S = π * R ^ 2 = π * a ^ 2/4 Cos2α.

Answer: The area of the circumscribed circle is π * a ^ 2/4 Cos2α.