Answer:
[tex]r_{1} = 26[/tex].
Step-by-step explanation:
Given : the ratio of the circumferences of two circles is 2:3. If the large circle has a radius of 39 cm,
To find : what is the radius of the small circle.
Solution : We have given that ratio of the circumferences of two circles is 2:3.
Let [tex]r_{2}[/tex] is radius of larger circle and [tex]r_{1}[/tex] is radius of small circle .
Then circumference = [tex]\frac{2\pi\ r_{1} }{2\pi\ r_{2}}[/tex] = [tex]\frac{2}{3}[/tex] .
Solving the above equation
[tex]\frac{r_{1}}{r_{2} }[/tex] = [tex]\frac{2}{3}[/tex] .
We have given radius of larger circle = 39 then
[tex]\frac{r_{1}}{39}[/tex] = [tex]\frac{2}{3}[/tex] .
On multiplying both sides by 39.
[tex]r_{1} = 39 *\frac{2}{3}[/tex].
[tex]r_{1} = 13 * 2[/tex].
[tex]r_{1} = 26[/tex].
Therefore, [tex]r_{1} = 26[/tex].
