Angle between Two Circles
Angle between Two Circles: Overview
This topic covers concepts such as Angle of Intersection of Two Circles, Common Chord of Two Circles, Equation of Common Chord of Two Circles, Length of Common Chord of Two Circles and Condition of Orthogonality of Two Circles.
Important Questions on Angle between Two Circles
The equation of the common chord of the pair of circles: and is

The equation of the circle which cuts orthogonally the circle and having the centre at is

The equation of the circle which passes through the points and orthogonal to the circle is

The equation of the circle passing through the origin, having its centre on the line and intersecting the circle orthogonally is

The equation of the circle which passes through the origin and intersects the circles, and orthogonally is

The equation of the circle which passes through the origin and intersects the circles, orthogonally: and is

The angle between the circles given by the equations: is

If the angle between the circles given by the equations: is , then write the value of .

Find if the following pairs of circles are orthogonal: .

Find if the following pairs of circles are orthogonal: .

Find if the following pairs of circles are orthogonal: .

Find if the following pairs of circles are orthogonal: .

In List-, a pair of circles is given in and in List-, angle between those pair of circles is given. Match the items from List- to List-
List- | List- | ||
(A) | I | ||
(B) | II | ||
(C) | III | ||
IV |

The possible number of values of for which the common chord of the circles and subtends a right angle at the origin is

Let be the common chord of the circles and , then the perimeter (in units) of the triangle is equal to

The locus of the centre of the circle which cuts the parabola orthogonally at will pass through the point

If the circles and are orthogonal then

If the angle between the circles and is , then is equal to

The length of the common chord of the two circles is

The length of the common chord of the two circles is
