Question

Two circles touch externally the sum of their areas is 130 per cm square and the distance between their centre is 14 cm find the radius of the circles

Answer 1

Answer:

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Answer 2

$\red\bigstar$QUESTION:-

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•Two circle touch externally the sum of the areas is 130πcm.and distance between there centre is 14cm.Find the radius of circle.

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$\blue\bigstar$SOLUTION:-

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•Since the given circle touch externally, we have

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⌖Sum of radii =distance between their centres =14cm

⌖Let the radii of the given circle be x cm and (14-x) cm .

$\sf \star Sum \: of \: their \: areas = \bf [ \pi x^{2}+ \pi(14-x)]cm^{2}$

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$\therefore \bf \pi x^{2}+ \pi(14-x)cm^{2} = 130\pi$

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$\bf \implies {x}^{2} + (14 - x)^{2} = 130$

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$\bf \implies2 {x}^{2} - 28x + 66 = 0$

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$\bf \implies {x}^{2} - 14x + 33 = 0$

•Factorising above by mid-term splitting method,⠀⠀⠀

$\bf \implies \bf(x - 11)(x - 3) = 0$

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$\bf \implies x - 11 = 0 \: \: or \: \: x - 3 =0$

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$\bf \implies \bf x = 11 \: \: or \: \: x = 3$

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Now, x=11 ⇨ (14-x)=(14-11)=3

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And , x=3 ⇨ (14-x)=(14-3)=11

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Hence, the radii of the given circles are 11cm and 3cm respectively