If the arcs of the same length in two circles | vedclass

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Question

$	heta=\frac{l}{r}$

$	heta ightarrow$ angle (in radians)

$l ightarrow$ are length

$r ightarrow$ radius

$l_{1}=l_{2}=l(\operatornam

Vedclass · Accepted Answer

$\frac{{64}}{{25}}$

Vedclass · Answer

$	heta=\frac{l}{r}$

$	heta ightarrow$ angle (in radians)

$l ightarrow$ are length

$r ightarrow$ radius

$l_{1}=l_{2}=l(\operatorname{say})$

$	heta_{1}=75^{\circ} \quad ; \quad 	heta_{2}=120^{\circ}$

$1^{0}=\left(\frac{\pi}{180}ight)^{c}$

$	heta_{1}=75^{\circ}=\left(\frac{5 \pi}{12}ight)^{	ext {radians }}$

$	heta_{1}=120^{\circ}=\left(\frac{2 \pi}{3}ight)^{	ext {radians }}$

$\frac{r_{1}}{r_{2}}=\frac{\frac{l_{1}}{	heta_{1}}}{\frac{\lambda_{2}}{	heta_{2}}}$

$=\frac{l_{1}}{	heta_{1}} 	imes \frac{	heta_{2}}{l_{2}}$

$r_{1}: r_{2}=8: 5$

If the arcs of the same length in two circles $S_1$ and $S_2$ subtend angles $75^o $ and $120^o $ respectively at the centre. The ratio $\frac{{{S_1}}}{{{S_2}}}$ is equal to

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