Geometry: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281159
ISBN 13: 978-0-13328-115-6

Chapter 10 - Area - 10-6 Circles and Arcs - Practice and Problem-Solving Exercises - Page 656: 51

Answer

$\dfrac{3}{4}$

Work Step by Step

$l=\dfrac{\text{Measure of the arc}}{360^{\circ}} \times 2 \pi r ~~~(a)$ or, $l=\dfrac{\text{Measure of the arc}}{360^{\circ}} \times \pi d~~(b)$ Here, $r$ represents radius and $d$ is diameter. Let us consider that $r_A$ and $r_B$ are the radii of circle $A$ and $B$. Since we have the same arc length, we can write: $\dfrac{60^{\circ}}{360^{\circ}} \times 2 \pi r_A=\dfrac{45^{\circ}}{360^{\circ}} \times 2 \pi r_B$ This gives: $60r_A=45 r_B$ or, $\dfrac{r_A}{r_B}=\dfrac{45}{60}=\dfrac{3}{4}$
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