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Question

If the pair of tangents are drawn from origin O to the circle x2+y26x8y+21=0, meets the circle at A and B , the lengths of AB is

A
11
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B
4521
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C
173
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D
215
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Solution

The correct option is A 4521
Given equation of circle is
x2+y26x8y+21=0,

whose centre =(3,4)

and radius =9+1621=2

Clearly, the line AB is chord of contact and its equation is

xx1+yy1+g(x+x1)+f(y+y1)+c=0

Here, (x1,y1)=(0,0)

0+03(x+0)4(y+0)+21=0

3x+4y21=0 ....(i)

Now, perpendicular distance from (3,4) to the line (i) is

CM=3(3)+4(4)219+16=45

AM=AC2CM2=41625=2521

AB=2AM=4521

703386_654890_ans_292ea1670d5c4d7191e75be720c68cbd.png

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