Circle

The tangent and the normal lines at the point $\left(\sqrt{3},1\right)$ to the circle $x^{2}+y^{2}=4$ and the $x$ -axis form a triangle. The area of this triangle (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

Points $P\left(-3,2\right),Q\left(9,10\right)$ and $R\left(\alpha\,,4\right)$ lie on a circle $C$ with $PR$ as its diameter. The tangents to $C$ at the points $Q$ and $R$ intersect at the point $S$. If $S$ lies on the…

A circle passing through the point$P\left(\alpha\,,\beta\,\right)$ in the first quadrant touches the two coordinate axes at the points$A$and$B.$ The point$P$is above the line$AB.$ The point$Q$on the line segment$AB$is…

The equation of the circle described on the chord $3x+y+5=0$of the circle $x^{2}+y^{2}=16$asthe diameter is

If two parallel chords of a circle, having diameter $4$units, lie on the opposite sides of the center and subtend angles $\cos\,^{-1}\left(\frac{1}{7}\right)$ and $\sec\,^{-1}\left(7\right)$ at the center respectively,…

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?

Let the centre of a circle, passing through the points $(0,0),(1,0)$ and touching the circle $x^2+y^2=9$, be $(h, k)$. Then for all possible values of the coordinates of the centre $(h, k), 4\left(h^2+k^2\right)$ is…

Let $O$be the origin and $OP$and $OQ$ be the tangents to the circle $x^{2}+y^{2}-6x+4y+8=0$at the points $P$and$Q$ on it. If the circumcircle of the triangle $OPQ$ passes through the point…

Let $B$ be the centre of the circle $x^{2}+y^{2}-2x+4y+1=0.$Let the tangents at two points $P$ and $Q$ on the circle intersect at the point $A(3,1).$Then…

Equations of two diameters of a circle are $2x-3y=5$and $3x-4y=7$. The line joining the points $\left(-\frac{22}{7},-4\right)$ and $\left(-\frac{1}{7},3\right)$ intersects the circle at only one point…

Let $AB$be a chord of length$12$ of the circle $\left(x-2\right)^{2}+\left(y+1\right)^{2}=\frac{169}{4}$ If tangents drawn to the circle at points $A$ and $B$ intersect at the point $P$, then five times the distance of…