Let PQ  and RS be Tangents At The Extremities Of A Diameter PR of A Circle Of Radius r. Such That PS and RQ intersect At A Point X on The Circumference Of The Circle, Then Diameter Of The Circle Equals. 

If the point (1, 4) lies inside the circle x² + y² – 6x – 10y + p = 0 and the circle does not touch or interest the coordinates axes, then

If the line x cos α + y sin α = p represents the common chord APQB of the circle x² + y² = a² and x² + y² = b² (a > b) as shown in the Fig, then AP is equal to

Two points P and Q are taken on the line joining the points A (0, 0) and B (3a, 0) such that AP = PQ = QB. Circles are drawn onAP, PQ, and QB as diameters. The locus of the point S, the sum of the squares of the lengths of the tangents from which to the three circles is equal to b², is

If OA and OB are two equal chords of the circle x² + y² – 2x + 4y = 0 perpendicular to each other and passing through the origin O, the slopes of OA and OB are the roots of the equation 

An equation of the chord of the circle x² + y² = a² passing through the point (2, 3) farthest from the centre is

The lengths of the intercepts made by any circle on the coordinates axes are equal if the centre lies on the line (s) represented by

A circle touches both the coordinates axes and the line  the coordinates of the centre of the circle can be

If the tangent at the point P on the circle x² + y² + 6x + 6y = 2 meets the straight line 5x – 2y + 6 = 0 at a point Q on the y-axis, then the length ofPQ is

If a > 2b > 0 then the positive value of m for which  is a common tangent to x² + y² = b² and (x – a)²+ y² = b² is   

A triangle PQR is inscribed in the circle x² + y² = 25. If Q and R have coordinates (3, 4) and (–4, 3) respectively, then ∠QPR is equal to