The length of minor widehat{AB} of a circle i | vedclass

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(C) The length of an arc $L$ is given by the formula $L = \frac{	heta}{360^{\circ}} 	imes 2\pi r$,where $	heta$ is the angle subtended at the centr

Vedclass · Accepted Answer

$90$

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(C) The length of an arc $L$ is given by the formula $L = \frac{	heta}{360^{\circ}} 	imes 2\pi r$,where $	heta$ is the angle subtended at the centre and $2\pi r$ is the circumference of the circle.Given that the length of the minor arc $\widehat{AB}$ is $\frac{1}{4}$ of the circumference,we have:$L = \frac{1}{4} 	imes (2\pi r)$Equating the two expressions for $L$:$\frac{	heta}{360^{\circ}} 	imes 2\pi r = \frac{1}{4} 	imes 2\pi r$Dividing both sides by $2\pi r$:$\frac{	heta}{360^{\circ}} = \frac{1}{4}$$	heta = \frac{360^{\circ}}{4} = 90^{\circ}$Therefore,the measure of the angle subtended by the minor arc $\widehat{AB}$ at the centre is $90^{\circ}$.

The length of minor $\widehat{AB}$ of a circle is $\frac{1}{4}$th of its circumference,then the measure of the angle subtended by minor $\widehat{AB}$ at the centre will be $\ldots .$ (in $^{\circ}$)

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