A circle C touches the line x = 2y at the point (2, 1) and intersects the circle

C₁ : x² + y² + 2y $$-$$ 5 = 0 at two points P and Q such that PQ is a diameter of C₁. Then the diameter of C is :

If a line along a chord of the circle 4x² + 4y² + 120x + 675 = 0, passes through the point ($$-$$30, 0) and is tangent to the parabola y² = 30x, then the length of this chord is :

Consider a circle C which touches the y-axis at (0, 6) and cuts off an intercept $$6\sqrt 5 $$ on the x-axis. Then the radius of the circle C is equal to :

Two tangents are drawn from the point P($$-$$1, 1) to the circle x² + y² $$-$$ 2x $$-$$ 6y + 6 = 0. If these tangents touch the circle at points A and B, and if D is a point on the circle such that length of the segments AB and AD are equal, then the area of the triangle ABD is equal to :