Question

Two circles touch internally. The sum of their areas is 116π cm^2 and distance between their centers is 6 cm. Find the radii of the circles.​

Answer 1

$\huge \bf \underline{ \underline{Question}}$

Two circles touch internally. The sum of their areas is 116π cm^2 and distance between their centers is 6 cm. Find the radii of the circles.

$\huge \bf \underline{ \underline{Answer}}$

Given:-

• Two circles touch internally.
• The distance between their certes = 6cm
• The radii of the outer and inner circles are r2 and r1 respectively.
• The sum of their areas = 116πcm²

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To Find:-

$\sf (r2 \: \: \: and \: \: \: r1) =?$

Solution:-

Since the circles touch internally, the distance between their certres = the difference e between their radii = 6cm

$\sf ∴ r2−r 1 =6cm$

$\sf ⟹r 2=r 1 + 6$

So area of outer circle,

$\sf =π×(r2)² = π×(r1 +6)²$

And area of inner circle,

$\sf =π×(r1)²$

∴The sum of their areas,

$\sf =π×(r1 +6)² +π×(r1)² =116π$

$\sf ⟹(r1 )² +6r − 40=0$

$\sf ⟹(r1+10)(r1−4)=0$

$\sf ⟹r1=(−10,4)cm$

We reject the negative value of r1 since r1 is a length.

$\sf ∴r1 =4cm$

So,

$\sf r2 =(r1 +6)cm=(4+6)cm=10cm$

$\sf ∴r1 =4cm,r2 =10cm$

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Answer 2

$\huge{ \red{ \fbox{↪ answer : }}}$

r2=(r1+6)cm=(4+6)cm=10cm

∴r1 =4cm,r2 =10cm∴r1=4cm,r2=10cm

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Mark upper one Brainliest $\huge\color{red}♡$