AP EAMCET Engineering 20 Apr 2019 Shift 2 Paper

Consider the equation of circle.
x2+y2−2x−4y−20=0
The equation of tangent at the point
B(1,7)
on the circle is,
x+7y−(x+1)−2(y+7)−20‌‌=0
5y‌‌=35
y‌‌=7
The equation of tangent at the point
D(4,−2)
on the circle is,
4x−2y−(x+4)−2(y−2)−20=0
3x−4y=20
Consider the figure shown below. The point of intersection of tangents is C(16,7)
Thus, the area of quadrilateral ABCD is
Area‌‌=2×

1

2

r√S1
‌‌=2×

1

2

×(5)√256+49−32−28−20
‌‌=5×√225
‌‌=75