Question

If two tangents are drawn to a circle circle from an external point, the
(i) they subtend equal angles at the centre
(ii) they are equally inclined to the segment, joining the centre to that point.

Answer 1

In $\Delta APO$ and $\Delta BPO$

$OA=OB$ (radii)

$AP=BP$ (theorem)

$OP=OP$ (common)

$\Delta APO\cong \Delta BPO$ (by SSS congruency)

by cpct,

$\angle AOP=\angle BOP$ (hence, they suntend equal angle at centre P)

$\angle APO=\angle BPO$ (hence, they are equally inclined)