A Circle Passes Through The Point (–1, 7) And Touches The Line y = x at (1, 1). Its Diameter Is

Let AB be a chord of the circle x² + y² = a² subtending a right angle at the centre. Then the locus of the centroid of the triangle PAB as Pmoves on the circle is

The lines joining the origin to the points of intersection of the line 4x + 3y = 24 with the circle (x – 3)² + (y – 4)² = 25 are

If the circles x² + y² + 2ax + cy + a = 0 and x² + y² – 3ax + dy – 1= 0 intersect in two distinct points P and Q then the line

5x + by – a = 0 passes through P and Q for:  

The intercept on the line y = x by the circle x² + y² – 2x = 0 is AB. Equation of the circle on AB as diameter is:

A square is formed by following two pairs of straight lines y² – 14y + 45 = 0 and x² – 8x + 12 = 0. A circle is inscribed in it. The centre of the circle is 

Let PQ and RS be tangents at the extremities the diameter PR of a circle of radius r. If PS and RQ intersect at a point X on the circumference of the circle, then 2r equals 

A diameter of x² + y² – 2x – 6y + 6 = 0 is a chord to circle (2, 1), then radius of the circle is 

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

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