"Two circles are concentric, and have radii of..." solved and explained

High School
Geometry
High school geometry
Circles

postillan4

Answered question

2021-08-16

Two circles are concentric, and have radii of 15 and 25 respectively. If two arcs are formed by the same central angle, what the following are possible arc lengths

Answer & Explanation

Ezra Herbert

Skilled2021-08-17Added 99 answers

Step 1
Given that two circle are concentric and have radii of 15 and 25 respectively.
We know that arc length

= \frac{θ}{360^{\circ}} \times 2 π \times r

From first circle

\frac{θ}{360^{\circ}} \times 2 π \times r_{1} = 15 \dots \dots . (1)

From the second circle

\frac{θ}{360^{\circ}} \times 2 π \times r_{2} = 25 \dots . . (2)

Step 2
Decide equation (1) by equation (2)

\frac{r_{1}}{r_{2}} = \frac{15}{25}

\Rightarrow \frac{r_{1}}{r_{2}} = \frac{3}{5}

So radius will be in the

\frac{3}{5}

ratio.
Hence, the possible arc lengths is

\frac{3}{5}, \frac{6}{10}, \frac{9}{15}, \dots \dots .

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