Find the length of the tangent from the point (5, 6) to the circle x² + y² = 9.

Find the centre and radius of the circle x² + y² − 6x + 4y − 12 = 0.

Find the equation of the circle passing through the origin with its centre at (3, 4).

Find the equation of the circle with the points (1, 2) and (5, 6) as the ends of a diameter.

Write the equation of the circle with centre (2, −3) and radius 4.

In a class of 60 students, 35 play cricket, 28 play football and 12 play both. How many play neither?

Prove that cos 2A = 1 − 2sin²A.