Question

The radii of two circles are 19 cm and 9 cm respectively.
Find the radius of the circle which has circumference equal
to the sum of the circumferences of the two circles.​

Answer 1

Answer:

28cm this is the radius of the required circle.

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Answer 2

Answer:

Given:

Radius of 1st circle, r₁ = 9 cm

Radius of 2nd circle, r₂ = 19 cm

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✇ Let the radius of required circle formed be r cm

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$\underline{\textsf{\textbf{According\:to\:question\::}}}$

Circumference of required circle = Sum of circumference of two circles

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$\underline{\:\bigstar\:{\textsf{Circumference\:of\:smaller\:circle\::}}}$

$:\implies\sf 2 \pi r_1$

$:\implies\sf 2 \pi \times 9$

$:\implies\sf 18 \pi$

$\underline{\:\bigstar\:{\textsf{Circumference\:of\:larger\:circle\::}}}$

$:\implies\sf 2 \pi r_2$

$:\implies\sf 2 \pi \times 19$

$:\implies\sf 38 \pi$

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Now,

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Circumference of required circle = Sum of circumference of two circles

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$\dashrightarrow\sf 2 \pi r = 2 \pi r_1 + 2 \pi r_2$

$\dashrightarrow\sf 2 \pi r = 18 \pi + 38 \pi$

$\dashrightarrow\sf 2 \pi r = 56 \pi$

$\dashrightarrow\sf r = \dfrac{56 \pi}{2 \pi}$

$\dashrightarrow{\underline{\boxed{\sf{r = 28\;cm}}}}\;\bigstar\;$

$\therefore\;{\underline{\sf{Hence,\; Radius\;of\;new\;circle,\;r\;is\; \bf{28\;cm}.}}}$