If common chord of the circle C with centre at (2, 1) and radius r and the circle x2 + y2 – 2x – 6y + 6 = 0 is a diameter of the second circle, then the value of r is  


Correct option is


Equation of the circle C is  

           (x – 2)2 + (y – 1)2 = r2

⇒        x2 + y2 – 4x – 2y + 5 – r2 = 0  

Equation of the common chord is


If it is a diameter of the second circle, it passes through the centre (1, 3) of the circle 



A line meets the coordinate axes in A and B. A circle is circumscribed about the triangle OAB. If m and n are the distances of the tangent to the circle at the origin from the points A and B respectively, the diameter of the circle is



If a circle passes through the point (ab) and cuts the circle x2 + y2 = k2 orthogonally, equation of the locus of its centre is


Equation of the circle which passes through the origin, has its centre on the line x + y = 4 and cuts the circle

x2 + y2 – 4x + 2y + 4 = 0 orthogonally, is


If O is the origin and OPOQ are distinct tangents to the circle x2 + y2 + 2gx + 2fy + c = 0, the circumcentre of the triangle OPQ is


The circle passing through the distinct points (1, t), (t, 1) and (tt) for all values of t, passes through the point


If OA and OB are the tangents from the origin to the circle x2 + y2 + 2gx + 2fy + c = 0, and C is the centre of the circle, the area of the quadrilateral OACB is 


The angle between a pair of tangents drawn from a point P to the circle x2 + y2 + 4x – 6y + 9 sin2α + 13 cos2α = 0 is 2α. The equation of the locus of the point P is


Equation of a circle through the origin and belonging to the co-axial system, of which the limiting points are (1, 2), (4, 3) is


If a line segment AM = a moves in the plane XOY remaining parallel toOX so that the left end point A slides along the circle x2 + y2 = a2, the locus of M is


Tangents drawn from the point P(1, 8) to the circle x2 + y2 – 6x – 4y – 11 = 0 touch the circle at the points A and B. The equation of the circumcircle of the triangle in PAB is