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The length of the direct common tangent to two circles of radii r₁ and r₂ and d is the distance between their centres is:

Question

The length of the direct common tangent to two circles of radii r₁
and r₂ and d is the distance between their centres is:

$\sqrt{d^2-(r₁r₂) }$

$\sqrt{d^2-(r_1 +r_2 )^2 }$

$\sqrt{d^2-(r_1^2 r_2^2 ) }$

$\sqrt{d^2-(r_1-r_2 )^2 }$

Solution

Correct option is D

Given:

Radii of two circles:

r_1

and

r_2

Distance between their centers: d

Solution:

\bf \text{Length of the direct common tangent} = \sqrt{d^2 - (r_1 - r_2)^2}

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The length of the direct common tangent to two circles of radii r₁
and r₂ and d is the distance between their centres is:

$\sqrt{d^2-(r₁r₂) }$

$\sqrt{d^2-(r_1 +r_2 )^2 }$

$\sqrt{d^2-(r_1^2 r_2^2 ) }$

$\sqrt{d^2-(r_1-r_2 )^2 }$

Correct option is D

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The length of the direct common tangent to two circles of radii r₁ and r₂ and d is the distance between their centres is:

​d2−(r1r2)\sqrt{d^2-(r₁r₂) }d2−(r1​r2​)​​​

​d2−(r1+r2)2\sqrt{d^2-(r_1 +r_2 )^2 }d2−(r1​+r2​)2​​​

​d2−(r12r22)\sqrt{d^2-(r_1^2 r_2^2 ) }d2−(r12​r22​)​​​

​d2−(r1−r2)2\sqrt{d^2-(r_1-r_2 )^2 }d2−(r1​−r2​)2​​​

Correct option is D

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The length of the direct common tangent to two circles of radii r₁
and r₂ and d is the distance between their centres is:

$\sqrt{d^2-(r₁r₂) }$

$\sqrt{d^2-(r_1 +r_2 )^2 }$

$\sqrt{d^2-(r_1^2 r_2^2 ) }$

$\sqrt{d^2-(r_1-r_2 )^2 }$