What is the circumference of the below circle given that AB is the diameter and XY is perpendicular to AB?

Find ?PRB. Given
I. ?BPQ = 22^? and O is the centre of the circle
II. ?RBP = 54^? and chord PQ is parallel to AB

The two sides of a triangle are 8 cm and 9 cm and one angle is 60^?. Which of the following can be the length of its third side?
I. √23 cm
II. √73 cm
III.(4.5 - √3.25) cm
IV. (4 + √33) cm
V. (9 + √13) cm

There is a set of parallel lines with x lines in it and another set of parallel lines with y lines in it. The lines intersect at 12 points. If x > y, find the maximum number of parallelograms that can be formed.

There are 2 concentric circles, one big and one small. A square ABCD is inscribed inside the big circle while the same square circumscribes the small circle. The square touches the small circle at points P, Q, R and S. Determine the ratio of circumference of big circle to the polygon PQRS.