Prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact.

In figure, $\mathrm{PO}\perp \mathrm{QO}$, the tangents to the circle with centre $\mathrm{O}$ at $\mathrm{P}$ and $\mathrm{Q}$ intersect at point $\mathrm{T}$. Prove that $\mathrm{PQ} \mathrm{and} \mathrm{OT}$ are right bisectors of each other.

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In figure, from an external point $\mathrm{P}$, two tangents, $\mathrm{PA}$ and $\mathrm{PB}$ are tangents to the circle with centre $\mathrm{O}$. If $\mathrm{CD}$ is another tangent at point $\mathrm{E}$ to the circle and $\mathrm{PA}=12 \mathrm{cm}$. Find the perimeter of $∆\mathrm{PCD}$.