List of top Mathematics Questions on Circle asked in JEE Main

Let a, b and c be the length of sides of a triangle ABC such that:
\(\frac {a+b}{7}=\frac {b+c}{8}=\frac {c+a}{9}\)
If \(r\) and \(R\) are the radius of incircle and radius of circumcircle of the triangle ABC, respectively, then the value of \(\frac Rr\) is equal to :
Let \(\frac{dy}{dx} = \frac{ax-by+a}{bx+cy+a}\), where a, b, c are constants, represent a circle passing through the point (2, 5). Then the shortest distance of the point (11, 6) from this circle is
The line y = x + 1 meets the ellipse \(\frac{x^2}{4}+\frac{y^2}{2}=1\) at two points P and Q. If r is the radius of the circle with PQ as diameter then (3r)2 is equal to
A circle touches both the y-axis and the line x + y = 0. Then the locus of its center is
Let a circle C touch the lines L1 : 4x – 3y +K1 = 0 and L2 : 4x – 3y + K2 = 0, K1, K2∈R. If a line passing through the centre of the circle C intersects L1 at (–1, 2) and L2 at (3, –6), then the equation of the circle C is :
Let the tangent to the circle C1: x2 + y2 = 2 at the point M(–1, 1) intersect the circle C2: (x – 3)2 + (y – 2)2 = 5, at two distinct points A and B. If the tangents to C2 at the points A and B intersect at N, then the area of the triangle ANB is equal to

Let a circle C : (x – h)2 + (y – k)2 = r2, k > 0, touch the x-axis at (1, 0). If the line x + y = 0 intersects the circle C at P and Q such that the length of the chord PQ is 2, then the value of h + k + r is equal to ____.

If the tangents drawn at the points O(0, 0) and P(1 + √5, 2) on the circle x2 + y2 – 2x – 4y = 0 intersect at the point Q, then the area of the triangle OPQ is equal to

Let C be a circle passing through the points A(2, –1) and B (3, 4). The line segment AB is not a diameter of C. If r is the radius of C and its centre lies on the circle
\((x−5)^2+(y−1)^2=\frac{13}{2}\)
then r2 is equal to

Let the tangents at two points A and B on the circle\( x^2 + y^2 – 4x + 3 = 0\) meet at origin O(0, 0). Then the area of the triangle OAB is
Let a point P be such that its distance from the point (5, 0) is thrice the distance of P from the point (-5, 0). If the locus of the point P is a circle of radius r, then 4r² is equal to ________
The number of common tangents to the circles $x^2+y^2-4x-6y-12=0$ and $x^2+y^2+6x+18y+26=0$
The circle x2+y2+4x−7y+12=0 cuts an intercept on y -axis of length
A circle passes through (0, 0) and (1, 0) and touches the circle x2 + y2 = 9. Then the locus of the centre of the circle is: