# The radius of a circle is 5 cm. A chord of length square root 50 cm is drawn in the circle. Find the area of the major segment. Answer given in the book is 71.375 square cm  Whereas my calculation gives 71.428 sq cm Kindly, check it? The radius of a circle is 5 cm. A chord of length square root 50 cm is drawn in the circle. Find the area of the major segment. Answer given in the book is 71.375 square cm  Whereas my calculation gives 71.428 sq cm Kindly, check it?

Dear Student,

From given information we form our diagram , As :

Here ,  OA  = OB  = 5  cm   and AB =  $\sqrt{50}$  and AC =  BC  = $\frac{\sqrt{50}}{2}$ as we know perpendicular from center ( OC ) is bisect the chord ( AB ) .

We know :  Sin

In $∆$ OCA and get

Similarly
$\angle$ BOC  =  45$°$ , So

$\angle$ AOB  =  $\angle$ AOC  +  $\angle$ BOC  =  45$°$ +  45 $°$  =  90$°$

We know area of sector of circle  = , So

Area of sector :
And

Area of $∆$ AOB  =

Then,

Area of minor segment = Area of sector  -  Area of $∆$ AOB  =

Therefore,

Area of major segment = Area of circle  -  Area of minor segment =
So answer provided by you is correct , Keep it up .

Hope this information will clear your doubts about Areas Related to Circles .

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