Question

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

• A. 150
• B. 75
• C. 75/2
• D. None of these

Answer 1

Answer: (B)

75

Answer 2

Here, centre is A (1,2), and Tangent at B (1,7) is x.l +y.l - 1 (x+ l)-2 (y + 7)-20 = 0 ory = 7 $\quad$ ...(1) Tangent at D (4,-2) is 3x-4y-20 = 0 $\quad$ ...(2) Solving (1) and (2), we get C is (16,7) Area ABCD = 2 (Area of A ABC) $\quad=2\times\frac{1}{2} AB\times BC$ $AB\times BC=5\times15=75 \, units$