A is the centre of the circle x^2+y^2-2 x-4 y-20=0 . If the tangents drawn at the points B(1,7) and D(4,-2) on the circle meet at the point C , then area of the quadrilateral A B C D (in square units) is

Step-by-step solution

Equation of the given circle is Now, equation of tangent at the point B(1,7) on the circle is x+7 y-(x+1)-2(y+7)-20=0 5 y=35 Similarly, equation of tangent at the point D(4,-2) on the circle is 4 x-2 y-(x+4)-2(y-2)-20=0 Now, point of intersection of tangents (ii) and (iii) is C(16,7) . Now, area of required quadrilateral A B C D aligned & =2 Area of A B C=2 1 2 r S₁ & [where r= radius of circle ( i ) & = 1+4+20 =5 & and S₁ = 256+49-32-28-20 & = 225 =15 ] =5 15=75 aligned Hence, option (a) is correct.