Two tangents are drawn from the point
Question:

Two tangents are drawn from the point $\mathrm{P}(-1,1)$ to the circle $x^{2}+y^{2}-2 x-6 y+6=0$. If these tangents touch the circle at points $A$ and $B$, and if $D$ is a point on the circle such that length of the segments $\mathrm{AB}$ and $\mathrm{AD}$ are equal, then the area of the triangle ABD is equal to:

  1. 2

  2. $(3 \sqrt{2}+2)$

  3. 4

  4. $3(\sqrt{2}-1)$


Correct Option: , 3

Solution:

$\triangle \mathrm{ABD}=\frac{1}{2} \times 2 \times 4$

$=4$

 

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