Question

Two tangents are drawn from the point $P(-1,1)$ to the circle $x^2+y^2-2x-6y+6=0.$ 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 $AB$ and $AD$ are equal, then the area of the triangle $ABD$ is equal to

• A. $2$
• B. $(3\sqrt{2}+2)$
• C. $4$
• D. $3(\sqrt{2}-1)$

Answer 1

The correct option is C $4$


Now, area of
$△ABD=2\times \left(△ACD\right)$
$\therefore △ABD=2\times (\frac{1}{2}\times 2\times 2)=4$