Circles question bank (Maths)

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

$PQ$ is a chord of length $8 \, cm$ of a circle of radius $5 \, cm$. The tangents at $P$ and $Q$ intersect at a point $T$ (see figure). Find the length $TP$.