How many tangents can be constructed from a point inside the circle?

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.

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 $AC$ is a tangent to the circle with centre $O$. If $\angle ADB=55°$, find $x and y$. Give reasons for your answers.

A circle can have _____ parallel tangent(s) at the most.

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:

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 $\angle OBC$

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 :

From an external point$T$, two tangents $TP$and $TQ$ are drawn to a circle having its centre ate$O$. Prove that $\angle PTQ=2\angle OPQ$.

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?