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In a circle of diameter 50cm,the length of a chord is 25cm.Find the length of the minor arc of the chord

$\begin{array}{1 1}(A)\;\large\frac{20\pi}{3}\normalsize cm\\(B)\;\large\frac{19\pi}{3}\normalsize cm\\(C)\;\large\frac{24\pi}{3}\normalsize cm\\(D)\;\large\frac{25\pi}{3}\normalsize cm\end{array} $

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  • Radian measure =$\large\frac{\pi}{180}\times $ Degree measure
  • $l=r\theta$
Here radius of the circle $r=\large\frac{50}{2}$$=25cm$
Let O be the centre of the circle and AB be the given chord such that AB=25cm
$\therefore \Delta OAB$ is equilateral
$\therefore\angle AOB=60^{\large\circ}=(60\times \large\frac{\pi}{180})$ radians
$\Rightarrow \large\frac{\pi}{3}$ radians
Let the length of the minor arc of chord AB be l,then
$\;\;=25\times \large\frac{\pi}{3}$
$\;\;=\large\frac{25\pi}{3}$ cm
Hence (D) is the correct answer.
answered May 20, 2014 by sreemathi.v

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