The Locus Of The Mid Points Of A Chord Of The Circles x2 + y2 = 4, Which Subtends A Right Angle At The Origin 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:

The circle x² + y² + x + y = 0 and x² + y² + x – y = 0 intersect at the angle of:

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

The tangents drawn from the origin to the circle x² + y² – 2kx – 2ry + r² = 0 are perpendicular, if:

The chord of contact of tangents from a point P to a circle passes through Q, if l₁ and l₂ are the lengths of tangents from P and Q to the circle, then PQ is equal to: