Circle

Let$C$ be a circle passing through the points $A\left(2,-1\right)$and $B\left(3,4\right)$. The line segment $AB$is not a diameter of $C$. If $r$is the radius of $C$ and its centre lies on the circle…

The sum of the squares of the lengths of the chords intercepted on the circle, $x^{2}+y^{2}=16,$ by the lines, $x+y=n,n\in\,N,$ where $N$ is the set of all natural numbers is:

If the angle of intersection at a point where the two circles with radii $5cm$ and $12cm$ intersect is $90^{\circ}$, then the length (in cm) of their common chord is:

If the tangents at the points $P$and $Q$on the circle $x^{2}+y^{2}-2x+y=5$meet at the point $R\left(\frac{9}{4},2\right),$then the area of the triangle $PQR$is

The set of values of $k$for which the circle $C:4x^{2}+4y^{2}-12x+8y+k=0$lies inside the fourth quadrant and the point $\left(1,-\frac{1}{3}\right)$lies on or inside the circle $C$is

Let $C$be the centre of the circle$x^{2}+y^{2}-x+2y=\frac{11}{4}$and $P$be a point on the circle. A line passes through the point $C$, makes an angle of $\frac{\pi\,}{4}$ with the line $CP$ and intersects the circle at…

A line drawn through the point $P\left(4,7\right)$ cuts the circle $x^{2}+y^{2}=9$ at the points$A$and $B$. Then $P_{A}\cdot\,P_{B}$ is equal to?

In the circle given below, let $OA=1$ unit, $OB=13$ unit and $PQ\perp\,OB$. Then, the area of the triangle $PQB$ (in square units) is :

If the tangents drawn at the point $O\left(0,0\right)$and $P\left(1+\sqrt{5},2\right)$on the circle $x^{2}+y^{2}-2x-4y=0$intersect at the point $Q$, then the area of the triangle $OPQ$ is equal to

Let a triangle $ABC$ be inscribed in the circle$x^{2}-\sqrt{2}\left(x+y\right)+y^{2}=0$such that$\angle\,BAC=\frac{\pi\,}{2}$. If the length of side$AB$is$\sqrt{2}$,then the area of the$\triangle\,ABC$is equal to:

Let $A=\left{\left(x,y\right)\in\,R\times\,R\mid\,2x^{2}+2y^{2}-2x-2y=1\right}$ $B=\left{\left(x,y\right)\in\,R\times\,R\mid\,4x^{2}+4y^{2}-16y+7=0\right}$and…

Let the tangents drawn to the circle, $x^{2}+y^{2}=16$ from the point$P\left(0,h\right)$ meet the $x$-axis at points$A$ and $B$. If the area of $\Delta\,APB$is minimum, then positive value of$h$ is: