The radii of two circles are 19, cm and 9, cm | vedclass

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(B) Radius $(r_1)$ of the $1^{st}$ circle $= 19\, cm$.Radius $(r_2)$ of the $2^{nd}$ circle $= 9\, cm$.Let the radius of the $3^{rd}$ circle be $r$.Ci

Vedclass · Accepted Answer

$28$

Vedclass · Answer

(B) Radius $(r_1)$ of the $1^{st}$ circle $= 19\, cm$.Radius $(r_2)$ of the $2^{nd}$ circle $= 9\, cm$.Let the radius of the $3^{rd}$ circle be $r$.Circumference of the $1^{st}$ circle $= 2\pi r_1 = 2\pi(19) = 38\pi$.Circumference of the $2^{nd}$ circle $= 2\pi r_2 = 2\pi(9) = 18\pi$.Circumference of the $3^{rd}$ circle $= 2\pi r$.According to the problem,the circumference of the $3^{rd}$ circle is equal to the sum of the circumferences of the first two circles:$2\pi r = 38\pi + 18\pi$$2\pi r = 56\pi$Dividing both sides by $2\pi$:$r = \frac{56\pi}{2\pi} = 28\, cm$.Therefore,the radius of the required circle is $28\, cm$.

Part $I$	Part $II$
$1.$ Formula to find the length of a minor arc	$a.$ $C=2\pi r$
$2.$ Formula to find the area of a minor sector	$b.$ $A=\pi r^{2}$
$3.$ Formula to find the area of a circle	$c.$ $l=\frac{\pi r \theta}{180}$
$4.$ Formula to find the circumference of a circle	$d.$ $A=\frac{\pi r^{2} \theta}{360}$

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. (in $cm$) [use $\pi=\frac{22}{7}$]

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