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Question

Let A be the centre of the circle x2+y22x4y20=0. Suppose that the tangents at the points B(1,7) and D(4,2) on the circle meet at the point C. Find the area of the quadrilateral ABCD

A
150sq. units
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B
75sq. units
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C
25sq. units
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D
100sq. units
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Solution

The correct option is B 75sq. units
Equation of tangent at B(1,7) and D(4,2) are

x+7y(x+1)2(y+7)20=05y=35y=7

and 4x2y(x+4)2(y2)20=03x4y=20

Therefore point C is (16,7)

Therefore the area of quadrilateral ABCD

=area of ΔABC+area of ΔACD

=12×15×5+12×15×5=75

348140_257418_ans_59d736c96752473397443c72e57b3833.png

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