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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.

$\begin{array}{1 1}(a)\;\large\frac{\pi}{3}\;\normalsize cm&(b)\;\large\frac{25\pi}{3}\;\normalsize cm\\(c)\;\large\frac{5\pi}{3}\;\normalsize cm&(d)\;\large\frac{7\pi}{3}\;\normalsize cm\end{array}$

1 Answer

Here radius of the circle $r=\large\frac{50}{2}$
$\qquad\qquad\qquad\qquad\quad=25cm$
Let $O$ be the centre of the circle and AB be the given chord such that $AB=25cm$
Now $OA=OB=r=25cm$
$AB=25cm$
$\Delta OAB$ is equilateral.
$\angle AOB=60^{\large\circ}$
$\quad\quad\;\;=\big(60\times \large\frac{\pi}{180}\big)$$radians$
$\quad\quad\;\;=\large\frac{\pi}{3}$$radians$
Let the length of the minor arc of chord AB be $l$ then
$l=r\theta$
$\;\;=25\times \large\frac{\pi}{3}$
$\;\;=\large\frac{25\pi}{3}$$cm$
Hence (b) is the correct answer.
answered Oct 17, 2013 by sreemathi.v
 

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