Mathematics - Circle Question with Solution | TestHub

The chord of contact from $P(-4,0)$ is $x=-1$, so $T_1(-1,\sqrt{3}),T_2(-1,-\sqrt{3})$ and $T_1{T}_2=2\sqrt{3}$. The diagonals of the rhombus bisect each other at $M(-1,0)$, so $P^{\prime }=(2,0)$ and $P{P}^{\prime }=6$. Area $△P{T}_1{P}^{\prime }=\frac{1}{2}\times 6\times \sqrt{3}=3\sqrt{3}$; area $△P^{\prime }{T}_1{T}_2=\frac{1}{2}\times 2\sqrt{3}\times 3=3\sqrt{3}$. Ratio 1 : 1, hence none of these.