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The radii of two circles are 19 cm and 9 cm respectively. The radius of the circle which has its circumference equal to the sum of the circumferences of the two circles is:​
  • a)
    28 cm
  • b)
    32 cm
  • c)
    26 cm
  • d)
    30 cm
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
The radii of two circles are 19 cm and 9 cm respectively. The radius o...
Given:
Radii of two circles = 19 cm and 9 cm
Let the radius of the third circle be 'r'

To find: Radius of the circle which has its circumference equal to the sum of the circumferences of the two circles.

Solution:
1. Circumference of a circle = 2πr
2. Circumference of first circle = 2π(19) = 38π
3. Circumference of second circle = 2π(9) = 18π
4. Sum of circumferences of two circles = 38π + 18π = 56π
5. To find the radius of the third circle, we need to equate its circumference with the sum of the circumferences of the other two circles.
6. So, 2πr = 56π
7. Solving for 'r', we get r = 28 cm.

Therefore, the radius of the circle which has its circumference equal to the sum of the circumferences of the two circles is 28 cm (Option A).
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Community Answer
The radii of two circles are 19 cm and 9 cm respectively. The radius o...
28 because
Let the radius of required circle =r cm

Radius of 1st circle r1​=9 cm

Radius of 2nd circle r2​=19 cm

As per the question 

Circumference of the required circle = Sum of circumference of two circles

Circumference of small circle =2πr1​

                                                  =2π×9

                                                  =18π

Circumference of small circle =2πr2​

                                                  =2π×19

                                                  =38π

Now,

Circumference of the required circle = Sum of circumference of two circles

2πr=18π+38π

2πr=58π

r=2π56π​

r=28 cm

Hence, radius of new circle is 28 cm.
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The radii of two circles are 19 cm and 9 cm respectively. The radius of the circle which has its circumference equal to the sum of the circumferences of the two circles is:a)28 cmb)32 cmc)26 cmd)30 cmCorrect answer is option 'A'. Can you explain this answer?
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