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High School
Geometry
High school geometry
Circles

Umaiza Hutton

Answered question

2022-03-01

Two circles are concentric. Two arcs are formed by the same central angle, with arc lengths of 54 and 81 respectively. What are the possible radii for the circles

Answer & Explanation

alenahelenash

Expert2022-03-10Added 556 answers

Given:Two circles are concentric.Two arcs are formed by the same central angle, with arc lengths of 54 and 81 resspectively.Let, the central angle is

θ

.so,

\Rightarrow \frac{l_{1}}{r_{1}} = \frac{l_{2}}{r_{2}}

\Rightarrow \frac{54}{r_{1}} = \frac{81}{r_{2}}

\Rightarrow \frac{54}{81} = \frac{r_{1}}{r_{2}}

\Rightarrow \frac{2}{3} = \frac{r_{1}}{r_{2}}

So, the radii are in the ratio of 2:3.So, possible radiis are

= 18 and 27

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