List of top Mathematics Questions on Circles asked in AP EAPCET

If the radical axis of the circles \(x^2+y^2+2gx+2fy+c=0\) and \(2x^2+2y^2+3x+8y+2c=0\) touches the circle \(x^2+y^2+2x+2y+1=0\), then:
The radical axis of two orthogonal circles is \(x+1=0\). If one of those circles is \(x^2+y^2=4\), then the equation of the other circle is:
The tangent to the circle \(C_1:x^2+y^2-2x-1=0\) at the point \((2,1)\) cuts off a chord of length \(4\) units from a circle \(C_2\) whose centre is \((3,-2)\). The radius of circle \(C_2\) is:
If the chord \(y=mx+1\) of the circle \(x^2+y^2=1\) subtends an angle \(45^\circ\) at the major segment of the circle, then the value of \(m\) is:
Equation of the circle with origin as centre and passing through the vertices of an equilateral triangle whose median is of length \(3\) is:
The centre of the circle which intersects the circles \[ x^2+y^2-8x+10y+5=0 \] and \[ x^2+y^2-2x+2y+1=0 \] orthogonally is:
The locus of the point which forms a right-angled triangle with the fixed points \((2,3)\) and \((5,1)\) is
Two circles, each of radius 5, touch at $(1,2)$. If the common tangent at the point of contact is $4x+3y=10$, then the equation of one of the circles is:
A circle C cuts the circles \(x^{2}+y^{2}-4x+6y+4=0\) and \(x^{2}+y^{2}+6x-4y+9=0\) orthogonally. If origin lies on this circle C, then the radius of the circle C is
If a circle \(S\) passes through \((a, b)\) and cuts the circle \(x^2 + y^2 = 4\) orthogonally, then find the locus of the center of \(S\).
Find the interval of \(\lambda\) for which exactly two common tangents can be drawn to \(x^2+y^2-4x-4y+6=0\) and \(x^2+y^2-10x-10y+\lambda=0\).
The sum of the squares of the lengths of the chords intercepted on \(x^2+y^2=16\) by the lines \(x+y=n, n \in \mathbb{N}\) is:
A variable circle passes through the fixed point \(A(p,q)\) and touches the X-axis. The locus of the other end of the diameter through A is
Let \( \theta \) be the angle between the circles \( x^{2}+y^{2}-4x+2fy-f=0 \) and \( x^{2}+y^{2}+2fx-4y-f=0 \). If \( \cos\theta=\frac{9}{16} \) and \( f\in\mathbb{Z} \), then the distance between the centres of these circles is
The line \( 5x-12y-4=0 \) cuts the circle \( x^{2}+y^{2}-2x+2y+c=0 \) at two points A, B. If \( AB=2\sqrt{3} \), then the length of the tangent drawn from the point (2, 1) to the given circle is
The perpendicular distance from origin to the tangent drawn at the point \( P(\frac{\pi}{4}) \) to the circle \( x^{2}+y^{2}-4x-4y+6=0 \) is
The sum of the slopes of the common tangents drawn to the circles \( x^{2}+y^{2}+4x-2y-11=0 \) and \( x^{2}+y^{2}-2x+6y+6=0 \) is
If \( 2x+y-2=0 \) and \( 6x-4y+1=0 \) are two normals of a circle S and the length of the perpendicular drawn from (2, 3) to the line \( 3x+4y-3=0 \) is the radius of S, then the interior point of the circle S among the following options is
The locus of the centre of a circle of radius 2 which rolls on the outside of the circle \( x^{2}+y^{2}+3x-6y-9=0 \) along its circumference is
If the equation of a circle passing through the point (2, 1) and the points of intersection of the circles $x^{2}+y^{2}+4x-6y-3=0$ and $x^{2}+y^{2}-2x+2y-2=0$ is $x^{2}+y^{2}+2gx+2fy+c=0$, then $2g+f=$
If a circle passing through the points $(1, 5)$ and $(4,0)$ makes equal intercepts on coordinate axes and if its centre lies in the first quadrant, then $\sqrt{4g^{2}-c^{2}}=$
If a tangent drawn to the circle $x^{2}+y^{2}-6x-8y-11=0$ is perpendicular to the line $3x + 4y + k = 0$, then the distance from the origin to this tangent is
If $L$ represents a normal drawn at the point $P\left(\frac{\pi}{4}\right)$ on the circle $x^{2}+y^{2}+6x-6y-14=0$, then the equation of the diameter of this circle which is perpendicular to $L$ is
The length of the intercept made by the circle $x^2 + y^2 - 10x + 4y + 9 = 0$ on the x-axis is:
The length of the tangent from the point $(3, 4)$ to the circle $x^2 + y^2 - 2x - 4y + 1 = 0$ is: