Find the length of the transverse common tangent to two circle of radii 8 cm and 3 cm, the centers of the circles be at a distance 13 cm is

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\sqrt{3} cm

2 \sqrt{3} cm

3 \sqrt{3} cm

4 \sqrt{3} cm

answer is D.

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Detailed Solution

Radius or first circle

r_{1} = 8 cm

Radius or second circle

r_{2} = 3 cm

Distance between the circles

d = 13 cm

Now, distance between two transverse common tangents can be given as,

= \sqrt{d^{2} - {(r_{1} + r_{2})}^{2}}

= \sqrt{(13)^{2} - (8 + 3)^{2}}

= \sqrt{169 - 121} = \sqrt{48}

The common tangent's length

= 4 \sqrt{3} cm

Option 4 is correct.

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