TP and TQ are tangents from T to a circle with centre O…

The two tangents drawn from an outside point T to a circle are equal: $TP = TQ$. In the right triangle OPT, $PT^2 = OT^2 - OP^2$. The line OT bisects the angle $PTQ$ and also the angle $POQ$. In the figure OPTQ, $\angle POQ + \angle PTQ = 180^\circ$. A tangent from an outside point has the same length on both sides of OT.