Find the radius of largest circle in the following figure if all the three small circles are identical of radius ' $r$ '

(\frac{\sqrt{2}}{3} + 1) r

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(\frac{2}{\sqrt{3}} - 1) r

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r (\frac{2}{\sqrt{3}} + 1)

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(\sqrt{\frac{2}{3}} + 1) r

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Solution

The correct option is A $r (\frac{2}{\sqrt{3}} + 1)$
$A B = 2 r$
Let O be circumcentre of $Δ A B C$ .
Then OC is the circumradius of $Δ A B C = \frac{A B}{2 sin ∠ A B C} = \frac{2 r}{2 sin 60^{0}} = \frac{2 r}{\sqrt{3}}$
$∴ O E = O C + E C = \frac{2 r}{\sqrt{3}} + r$

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Find the radius of largest circle in the following figure if all the three small circles are identical of radius 'r'

The correct option is A r(2√3+1)AB=2r Let O be circumcentre of ΔABC.Then OC is the circumradius of ΔABC=AB2sin∠ABC=2r2sin600=2r√3∴OE=OC+EC=2r√3+r

Find the radius of largest circle in the following figure if all the three small circles are identical of radius ' $r$ '

The correct option is A $r (\frac{2}{\sqrt{3}} + 1)$
$A B = 2 r$
Let O be circumcentre of $Δ A B C$ .
Then OC is the circumradius of $Δ A B C = \frac{A B}{2 sin ∠ A B C} = \frac{2 r}{2 sin 60^{0}} = \frac{2 r}{\sqrt{3}}$
$∴ O E = O C + E C = \frac{2 r}{\sqrt{3}} + r$