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Question

Let A be the centre of the circle x2+y22x4y20=0. Let B(1,7) and D(4,2) be two points on the circle such that tangents at B and D meet at C. The area of the quadrilateral ABCD is
  
 
  1. 150 sq. units  
  2. 50 sq. units    
  3. 75 sq. units    
  4. 70 sq. units    


Solution

The correct option is C 75 sq. units    
Equation of tangent at B(1,7) is,
x+7y(x+1)2(y+7)20=0y=7
Equation of tangent at D(4,2) is,
4x2y(x+4)2(y2)20=03x4y=20

The coordinate of C will be,
=(16,7)
So,
BC=15

Area of quadilateral ABCD is,
=2×12×5×15=75 sq. units

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