The Circle x2 + y2 + x + y = 0 And x2 + y2 + x – y = 0 Intersect At The Angle Of:

If α, β, γ, δ be four angles of a cyclic quadrilateral taken in clockwise direction then the value of  will be:

A square is inscribed in the circle x² + y² – 2x + 4y + 3 = 0. Its sides are parallel to the co-ordinate axes. Then one vertex of the square is

A circle passes through the point (–1, 7) and touches the line y = x at (1, 1). Its diameter is

Let ABCD be a quadrilateral with area 18, with side AB parallel to the side CD and AB = 2CD. Let AD be perpendicular to AB and CD. If a circle is drawn inside the quadrilateral ABCD touching all the sides, then its radius is

Let a circle be given by 2x(x – a) + y(2y – b) = 0, (a ≠ 0, b ≠ 0). Find the condition on a and b, if two chords each bisected by the x – axis can be drawn to the circle from 

The equation of the locus of the mid points of the chords of the circle 4x² + 4y² – 12x + 4y + 1 = 0 that subtend an angle of  at its centre is:

Find the radius of the smallest circle which touches the straight line 3x– y = 6 at (1, –3) and also touches the line y = x. complete up to one place of decimal.

Let S ≡ x² + y² + 2gx + 2fy + c = 0 be a given circle. find the locus of the foot of the perpendicular drawn from the origin upon any chord of S which subtends a right angle at the origin.

The normal 3x – 4y = 4 and 6x – 8y – 7 = 0 are tangents to the circle. Then its radius is:

Find the radical centre of the circles, x² + y² + 3x + 2y + 1 = 0,  x² + y² – x + 6y + 5 = 0, x² + y² + 5x – 8y + 15 = 0