If the arcs of the same lengths in the two circles subtend angles 65°

1.	If the arcs of the same lengths in the two circles subtend angles 65° and 110° at the center, find the ratio of their radii.
Answer» We have l = rθ, the radius and angle are inversely proportional. Therefore; \(\frac{\theta_1}{\theta_2} = \frac{r_2}{r_1}\) \(\Rightarrow\)\(\cfrac{\frac{\pi}{180} \times 65}{\frac{\pi}{180} \times 110}\) = \(\frac{r_2}{r_1}\) \(\Rightarrow\) \(\frac{13}{22} = \frac{r_2}{r_1}\) \(\Rightarrow\) r₁ : r₂= 22: 13

If the arcs of the same lengths in the two circles subtend angles 65° and 110° at the center, find the ratio of their radii.

Answer»

We have l = rθ, the radius and angle are inversely proportional. Therefore;

\(\frac{\theta_1}{\theta_2} = \frac{r_2}{r_1}\)

\(\Rightarrow\)\(\cfrac{\frac{\pi}{180} \times 65}{\frac{\pi}{180} \times 110}\) = \(\frac{r_2}{r_1}\)

\(\Rightarrow\) \(\frac{13}{22} = \frac{r_2}{r_1}\)

\(\Rightarrow\) r₁ : r₂= 22: 13

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If the arcs of the same lengths in the two circles subtend angles 65° and 110° at the center, find the ratio of their radii.

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