Question

Prove that the lengths of the two tangent segments to a circle drawn from external point are equal

Answer 1

Given: $PT$ and $TQ$ are two tangents drawn from an external point $T$ to the circle $(O,r)$.

To prove: $PT=TQ$

Construction : Join $OT$

Proof:

$\therefore \angle OPT=\angle OQT={90}^o$

In $△OPT$ and $△OQT$,

$OT=OT$ ..... Common

$OP=OQ$ ....Radius of the circle

$\angle OPT=\angle OQT$ ....$\left({90}^o\right)$

$\therefore △OPT\cong △OQT$ ....RHS congruency test

$\therefore PT=TQ$ ....CPCT