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,

Please find below the solution to the asked query:

From given information we form our diagram , As :



Here ,  OA  = OB  = 5  cm   and AB =  50  and AC =  BC  = 502 as we know perpendicular from center ( OC ) is bisect the chord ( AB ) .

We know :  Sin θ = OppositeHypotenuse

In OCA and get

Sin   AOC  = ACOASin   AOC  = 5025Sin   AOC  = 505 × 2Sin   AOC  = 5 ×25 × 2× 2Sin   AOC  = 12Sin   AOC  = Sin 45° AOC =45°
Similarly
BOC  =  45° , So

AOB  =  AOC  +  BOC  =  45° +  45 °  =  90° 

We know area of sector of circle  = θ360°×π r2 , So

Area of sector : 90°360°×227 ×52 = 14×227 ×25= 14×227 ×25 = 27514 cm2
And

Area of AOB  = 12×Base × Height = 12× 5 × 5 = 252 cm2

Then,

Area of minor segment = Area of sector  -  Area of AOB  = 27514 - 252 = 275 - 17514 = 10014 = 507 cm2

Therefore,

Area of major segment = Area of circle  -  Area of minor segment = 227 × 5 ×5 - 507 = 5507- 507  = 5007 = 71.428 cm2
So answer provided by you is correct , Keep it up .

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

If you have any more doubts just ask here on the forum and our experts will try to help you out as soon as possible.

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