question_answer

Let A be the centre of the circle \[{{x}^{2}}+{{y}^{2}}-2x-4y-20=0,\] and \[B(1,7)\] and \[D(4,-2)\] are points on the circle then, if tangents be drawn at B and D, which meet at C, then area of quadrilateral ABCD is-

A) 150

B) 75

C) 75/2

D) None of these

Correct Answer: B

Solution :

[b] Here, centre is \[A(1,2)\], and tangent at \[B(1,7)\] is \[x.1+y.7-1(x+1)-2(y+7)-20=0\]            ?. (1) Or \[y=7\] Tangent at \[D(4,-2)\] is \[3x-4y-20=0\]                           ?. (2) Solving (1) and (2), we get C is \[(16,7)\] Area \[ABCD=2(Area\,\,of\,\Delta ABC)=2\times \frac{1}{2}AB\times BC\] \[=AB\times BC=5\times 15=75\] units