Interaction between Circle and a Line
Interaction between Circle and a Line: Overview
This topic covers concepts, such as Interaction between Line and a Circle, Position of a line with respect to a circle, Condition For Tangency to a Circle, Chord of a Circle, Length of the Chord of a Circle, Image of a Circle in a Line Mirror, etc.
Important Questions on Interaction between Circle and a Line
Find the point on the straight line, y = 2x + 11 which is nearest to the circle,

One of the diameters of the circle circumscribing the rectangle is . If and are the points and , respectively, then the area of the rectangle is

All the chords of the curve which subtend a right angle at the origin, pass through a fixed point. Find the coordinates of the point.

The points of intersection of the line and the circle are:

touches the circle . The equation of other parallel tangent is

The point where the line touches the circle .

If are the slopes of the tangents drawn from a point to the circle then

The length of the intercept on the line by the circle is

The points of intersection of the line and the circle are

Let be a circle passing through the points and . The line segment is not a diameter of . If is the radius of and its centre lies on the circle , then is equal to:

In the given figure, is a cyclic quadrilateral such that and , then find the measure of .

The radius of a circle whose center lies in the fourth quadrant and touches each of the three lines and is ............ units.

The length of the chord intercepted by the circle on the line is ______ units.

If the parametric values of two points on the circle are and , respectively, then the equation of chord is _______

Equation of the circle, which is the mirror image of the circle with respect to the line , is

If one of the diameters of the circle is a chord to the circle with centre , then the radius of the circle is

The circle cuts -axis at

The locus of centre of a circle which passes through the origin and cuts off a length of unit from the line is

Radius of circle in which a chord length makes an angle at the centre, is

If a chord of circle of radius unit is trisected at points & , then the distance of the chord from centre is
