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If 't(1)' , 't(2)' and 't(3)' are the le...

If `'t_(1)' , 't_(2)' and 't_(3)'` are the lengths of the tangents draen from centre of x-circle to the circumcircle of the `DeltaABC,` then `(1)/(t _(1)^(2))+(1)/(t _(2)^(2))+(1)/(t_(3)^(2))` is equal to

A

`(abc)/(a+b+c)`

B

`(a+b+c)/(abc)`

C

`(a+b+c)/(2abc)`

D

`(2 abc)/(a+b+c)`

Text Solution

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The correct Answer is:
B
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t_(1),t_(2),t_(3) are lengths of tangents drawn from a point (h,k) to the circles x^(2)+y^(2)=4,x^(2)+y^(2)-4=0andx^(2)+y^(2)-4y=0 respectively further, t_(1)^(4)=t_(2)^(2)" "t_(3)^(2)+16 . Locus of the point (h,k) consist of a straight line L_(1) and a circle C_(1) passing through origin. A circle C_(2) , which is equal to circle C_(1) is drawn touching the line L_(1) and the circle C_(1) externally. The distance between the centres of C_(1)andC_(2) is

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ARIHANT MATHS-PROPERTIES AND SOLUTION OF TRIANGLES -Exercise (Single Option Correct Type Questions)
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