Question

Let $A$ be the centre of the circle $x^2+y^2-2x-4y-20=0$. Let $B(1,7)$ and $D(4,-2)$ be two points on the circle such that tangents at $B$ and $D$ meet at $C$. The area of the quadrilateral $ABCD$ is

• A. $150$ sq. units
• B. $50$ sq. units
• C. $75$ sq. units
• D. $70$ sq. units

Answer 1

Answer: (C)

$75$ sq. units

tangent at $B,y=7$
tangnet at $D,x=16$
so $BC=15$
$\Rightarrow$ area of quadrilateral $=2\times \frac{1}{2}\times 5\times 15=75$