$P$ is a point in the exterior of $\odot(O, r)$ and the tangents from $P$ to the circle touch the circle at $X$ and $Y$. Find $OP$,if $r = 12$ and $XP = 5$.

$A$ tangent to a circle intersects the circle in $\ldots \ldots \ldots .$

$AB$ is a diameter of a circle. $l_{1}$ and $l_{2}$ are tangents to the circle drawn at points $A$ and $B$ respectively. Then,which of the following is true?

Two tangents $TP$ and $TQ$ are drawn to a circle with centre $O$ from an external point $T$. Prove that $\angle PTQ = 2 \angle OPQ$.

$A$ line passing through the centre of the circle $O$ intersects the tangent to the circle at $Q$. $P$ is the point of contact. If the radius of the circle is $9$ and $PQ = 40$,then find $OQ$.

Draw a circle and two lines parallel to a given line such that one is a tangent and the other is a secant to the circle.