An Equilateral Triangle Is Inscribed In The Circle x2 + y2 = a2 with The Vertex At (a, 0). The Equation Of The Side Opposite To This Vertex Is

If O is the origin and OP, OQ 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 (t, t) 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

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  

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

Let ABCD be a quadrilateral with area 18, with side AB parallel to 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

The lines 2x – 3y = 5 and 3x – 4y = 7 are the diameters of a circle of area 154 square units. An equation of this circle is (π = 22/7)