Prove that if two circles touch each other externally, then their centres and the point of contact are collinear.

Prove that the lengths of tangents drawn from an external point to a circle are equal.

In the given figure $PQ \& RS$ are two parallel tangents to a circle with centre $O$ and another tangent $AB$ with point of contact $C$ intersecting $PQ$ at $A$ and $RS$ at $B$. Prove that $\angle AOB=90°$.

In the figure, $\mathrm{O}$ is the centre of a circle, $\mathrm{AC}$ is a diameter. If $\angle \mathrm{ACB} = 50°$, then find the measure of $\angle \mathrm{BAC}$(in $°$).