Question

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

• A. 75 sq. unit
• B. 145 sq. unit
• C. 150 sq. unit
• D. 50 sq. unit

Answer 1

The correct option is A 75 sq. unit

Centre of the circle is A (1, 2)
Equation of the tangent at B (1, 7) is y = 7 $\to$ (1)
Equation of the tangent at D (4, - 2) is 3x - 4y - 20 = 0 $\to$ (2)
Point of intersection of the lines (1) and (2) is C(16, 7)
Area of ABCD=$\frac{1}{2}\left|\begin{array}{cc}(1-16)& (2-7)\\ (1-4)& (7+2)\end{array}\right|=\frac{1}{2}\left|\begin{array}{cc}-15& -5\\ -3& 9\end{array}\right|=\frac{1}{2}|-135-15|=75$