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Question

# The area of the quadrilateral formed by the tangent from the point (4,5) to the circle x2+y2−4x−2y−c=0 with a pair of radii joining the points of contacts of these tangents is 8 sq. units. The value of c is

A
12
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B
1
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C
3
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D
11
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Solution

## The correct options are C 11 D −1Given equation of circle is x2+y2−4x−2y−c=0(−g,−f)=(2,1)Radius =√g2+f2−c, h of sub tangent Length of subtangent from point (x1,y1)=√x21+y21−4x1−2y1−c Area of quadrilateral = length of subtangent x radius⇒√42+52−4×4−2×5−c×√4+1+c⇒82=(15−c)(5+c)⇒c2−10c−11=0⇒c=11,−1

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