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 = and AC = BC = as we know perpendicular from center ( OC ) is bisect the chord ( AB ) .
We know : Sin
In OCA and get
Similarly
BOC = 45 , So
AOB = AOC + 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 .
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.
Regards
Please find below the solution to the asked query:
From given information we form our diagram , As :
Here , OA = OB = 5 cm and AB = and AC = BC = as we know perpendicular from center ( OC ) is bisect the chord ( AB ) .
We know : Sin
In OCA and get
Similarly
BOC = 45 , So
AOB = AOC + 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 .
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.
Regards