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Question

If the lengths of the tangents from two points A, B to a circle are 6, 7 respectively. If A, B are conjugate points then AB =

A
5
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B
85
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C
852
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D
none
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Solution

The correct option is B 85
Let the equation of the circle be x2 + y2=a2 and A (x1,y1), B(x2,y2)
A, B are conjugate points x1x2+y1y2=a2 (1)
Length of the tangents from A, B are 6, 7 respectively x21+y21a2 = 6, x22+y22a2= 7
x21+y21a2 = 36
x22+y22a2 = 49
x21+y21+x21+y222a2 = 85
x21+y21+x21+y222
(x1 x2 + y1 y2) = 85 [From (1)]
(x21+x222x1x2) + (y21+y222y1y2) = 85 (x1x2)2 + (y1y2)2 = 85 AB2 = 85 AB = 85

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