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(C) The area of a sector of a circle is given by the formula $A = \frac{	heta}{360^\circ} 	imes \pi r^2$.Let the radii of the two circles be $r_1$ a

Vedclass · Accepted Answer

$2:3$

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(C) The area of a sector of a circle is given by the formula $A = \frac{	heta}{360^\circ} 	imes \pi r^2$.Let the radii of the two circles be $r_1$ and $r_2$ and the central angles be $	heta_1$ and $	heta_2$.Given that $	heta_1 = 	heta_2 = 	heta$.The ratio of the areas of the two sectors is given as $\frac{A_1}{A_2} = \frac{4}{9}$.Substituting the formula,we get $\frac{\frac{	heta}{360^\circ} 	imes \pi r_1^2}{\frac{	heta}{360^\circ} 	imes \pi r_2^2} = \frac{4}{9}$.Simplifying the expression,we have $\frac{r_1^2}{r_2^2} = \frac{4}{9}$.Taking the square root on both sides,we get $\frac{r_1}{r_2} = \sqrt{\frac{4}{9}} = \frac{2}{3}$.Therefore,the ratio of the radii is $2:3$.

Two minor sectors of two distinct circles have the measure of the angle at the centre equal. If the ratio of their areas is $4:9,$ then the ratio of the radii of the circles is ........

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