Question

If two tangents PA and PB are drawn to a circle with centre O from an external point P (figure), then match the column.

Answer 1

Given that $\angle APB=\theta ,$ we have also been given that PA and PB are tangents.
Thus since angle between radius and tangent is ${90}^0(B\to 1)$,we get $\angle AOB$ to be $180-\theta$ as sum of all angles of a quadrilateral(PAOB) is ${360}^0.$
$\therefore$ $D\to 4.$
Now triangle OAB is isosceles.
$\therefore$ $\angle OAB$ $=\angle OBA=\theta /2.$Thus $C\to 2.$
$\angle PAO=\angle PAB+\angle BAO$
$\therefore$ ${90}^0=\angle PAB+\theta /2$
Thus $A\to 3.$