The number of tangent which can be drawn from the point $\left(-1,\mathrm{ }2\right)$ to the circle ${\mathrm{x}}^2+{\mathrm{y}}^2+2\mathrm{x}-\mathrm{ }4\mathrm{y}+4=0$ is -

From a point $P$ outside a circle, $PAB$ is a secant and $PT$ is a tangent to the circle, where $A, B$ and $T$ are points on the circle. If $PT=5 cm, PA=4 cm$ and $AB=x cm$, then $x$ is equal to :

In the given figure, AP and BP are tangents to a circle with centre O. If $\angle APB={62}^{\circ }$ then the measure of $\angle AQB$ is:

Consider the following diagram in which $AB$ is the tangent to circle. Find the length of $OQ(in cm)$ if the measure of the largest chord of that circle is $6 cm$ and $PQ$ is $4 cm.$

In the given figure $TP$ and $TQ$ are two tangents to the circle with centre $O$, touching at $A$ and $C$ respectively. If $\angle BCQ=55°$ and $\angle BAP=60°$, find $\angle OBA$ and $\angle OBC$

In the given figure, $\angle QRN=40°, \angle PQR=46°$ and $MN$ is a tangent at $R$. What is the value(in degrees) of $x, y$ and $z$ respectively?

In the given figure $TP \& TQ$ are two tangents to the circle with centre $O$, touching at $A \& C$ respectively. If $\angle BCQ=55° \& \angle BAP=60°$, find $\angle ATC$ in degrees.