A, B, C, are three points on the circumference of a circle and if $AB = AC = 5\sqrt{2}$, angle $BAC = 90$ degrees then radius of the circle is __________.

The area of a circle is numerically equal to its circumference. Find the diameter of the circle.

Find the area of the largest circle that can be drawn inside a rectangle with sides 8 m $\times$ 9 m.

Find the value of x in the adjoining figure, if it is given that PR and QS are diameters of the circle.

The circumference of a circular field is 396 m and that of the other circular field is 132 m. Find the area (in m$^2$) of the third circular field whose radius is the sum of the radii of the first two fields. Take $\pi = \frac{22}{7}$

If point P(4, 2) lies on the circle having centre O(-1, 1), and C is the circumference of the circle, then value of $49C^2$, is:

AB is a diameter of a circle with centre (3, 4). If coordinates of A is the point (4, 9), then find the coordinates of B.