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Question

Let A be the centre of the circle x2+y2 - 2x - 4y - 20 = 0. Suppose that the tangents at the points B(1, 7) and D(4, - 2) on the circle meet at the point C. The area of the quadrilateral ABCD is

A
75 sq. unit
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B
145 sq. unit
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C
150 sq. unit
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D
50 sq. unit
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Solution

The correct option is A 75 sq. unit
Centre of the circle is A (1, 2)
Equation of the tangent at B (1, 7) is y = 7 (1)
Equation of the tangent at D (4, - 2) is 3x - 4y - 20 = 0 (2)
Point of intersection of the lines (1) and (2) is C(16, 7)
Area of ABCD=12(116)(27)(14)(7+2)=1215539=12|13515|=75

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