Find the area of the shaded region in terms of pi. O and P are the centers of the circle
Assuming that the 90 deg refers to the arc of the small circle,calculate its segment.Then find the arc of the big circle and calculate its segment.Add the two.Draw the radii of the circles to the points of intersection of the circles.The solution is simple.Try it
First look at this webpage.
The on that page is the line segment determined by the two points of intersections of the circles.
Then you can find the areas of the two halves.
I looked at your reference which I think is not going to help a high school geometry student.If the student draws the complete figure and knows the properties of special right triangles the solution to the arc of the big circle becomes apparent.I assume the student knows the difference between a sector and a segment