I labeled key vertices for convenience. Since OA is a radius meeting a point of tangency angle OAB is a right angle. Hence we can use the Pythagorean Theorem to find X. (OB is the hypotenuse) Since we have all three side lengths, we can calculate the area of triangle OAB directly.

Next we can find the area of the light blue wedge AOC. We can find the angle AOC using triangle OAB as reference using trigonometry. Then use the area formula that involves the angle and the radius OA to find the area of the light blue wedge

Triangle OAB - Wedge AOC = half the area of the desired region. Hence

2 (Triangle OAB - Wedge AOC) = the area of the desired region.