Question

Consider a circle $x^2+y^2-2x-4y-20=0$ with centre $A$. If the tangents to the circle at points $B(1,7)\text{and}C(4,-2)$ meet at a point $D$, then the area of the quadrilateral $ABDC$ is

• A. 75
• B. 75.00
• C. 75.0

Answer 1

Answer: (A), (B), (C)

Tangents at $B\text{and}C$ are $y=7\text{and}3x-4y-20=0$ respectively, they intersect at $D(16,7)$

Area of $ABDC=2\left(\text{area of triangle}ABD\right)$

$=\left|\begin{array}{ccc}1& 2& 1\\ 1& 7& 1\\ 16& 7& 1\end{array}\right|=75$