What is the radius of the circle whose circumference is equal to the sum of the circumference of the circles having radius 19 cm and 9 cm?options:

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What is the radius of the circle whose circumference is equal to the sum of the circumference of the circles having radius 19 cm and 9 cm?

options:

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28 cm

30 cm

26 cm

24 cm

answer is A.

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Detailed Solution

Concept- Assume that a variable will stand in for the radius of the circle whose circumference is equal to the sum of the circumferences of the circles with radius

and

. For a circle with radius equal to

, the circumference is given by the formula

. Using this formula, the question can be solved.
Before proceeding with the question, we must know all the formulas that will be required to solve this question.
Consider a circle having its radius equal to

. To find the circumference of this circle, we use the formula,

In the question, we have to find the radius of the circle whose circumference is equal to the sum of the circumference of the circles having radius

and

.
Let's say that this circle has the following radius: By applying formula (1), this circle's circumference is,

Using formula (1), the circumference of the circle with radius

is equal to,

Using formula (1), the circumference of the circle with radius

is equal to,

In the question, it is given that,

Substituting C from equation (2),

from equation (3) and

from equation (4) in the above equation, we get,