Let a be an integer multiple of 8. If S is the set of all possible values of a such that the line 6x + 8y + a = 0 intersects the circle x2 + y2 - 4x - 6y + 9 = 0 at two distinct points, then the number of elements in S is

Find the length of the diameter of the circle x2 + y2 - 6x - 8y = 0.

AB is a chord of a circle and AOC is its diameter such that ∠ACB = 65°. If AT is the tangent to the circle at the point A, then ∠BAT is equal to:

CP and CQ are tangents drawn from an external point C to a circle with centre O. ARB is another tangent touching the circle at R. If CP = 15 cm and BC = 8 cm, then the length of BR is: