Que. 16 (Question:656398.0)

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Abhilash Rathod

· started a discussion

· 1 Months ago

Que. 16 (Question:656398.0)

Option 1 and 3 are same.

Question:

The distance between the centres of two circles is 24 cm. If the radius of the two circles are 4 cm and 8 cm, then what is the sum of the lengths (in cm) of the direct common tangent and the transverse common tangent?

Options:

4(3√3 + √35)

4(4√35 + 3√3)

4(√35 + 3√3)

4√3(√35 + 3√3)

Solution:

d = 24cm

r₁ = 8cm

r₂ = 4cm

Length of direct common tangent

$\begin{matrix} = \sqrt{d^{2} - {(r_{1} - r_{2})}^{2}} \\ = \sqrt{576 - 16} \\ = 4 \sqrt{35} \end{matrix}$

Length of transverse common tangent

$\begin{matrix} = \sqrt{d^{2} - {(r_{1} + r_{2})}^{2}} \\ = \sqrt{576 - 144} \\ = 12 \sqrt{3} \end{matrix}$

Required sum = $4 \sqrt{35} + 12 \sqrt{3}$

$= 4 (\sqrt{35} + 3 \sqrt{3})$

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Que. 16 (Question:656398.0)

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