Example 3 - Find the area of segment AYB, if radius 21 cm - Examples

  1. Chapter 12 Class 10 Areas related to Circles
  2. Serial order wise
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Example 3 Find the area of the segment AYB shown in figure, if radius of the circle is 21 cm and โˆ AOB = 120ยฐ. (Use ฯ€ = 22/7 ). In a given circle, Radius (r) = 21 cm And, ๐œƒ = 120ยฐ Area of segment AYB = Area of sector OAYB โ€“ Area of ฮ”OAB Area of sector OAYB = ๐œƒ/360ร—๐œ‹๐‘Ÿ2 = 120/360ร—22/7ร—(21)2 = 1/3ร—22/7ร—21ร—21 = 22 ร— 21 = 462 cm2 Finding area of ฮ” AOB Area ฮ” AOB = 1/2 ร— Base ร— Height We draw OM โŠฅ AB โˆด โˆ  OMB = โˆ  OMA = 90ยฐ In ฮ” OMA & ฮ” OMB โˆ  OMA = โˆ  OMB OA = OB OM = OM โˆด ฮ” OMA โ‰… ฮ” OMB โ‡’ โˆ  AOM = โˆ  BOM โˆด โˆ  AOM = โˆ  BOM = 1/2 โˆ  BOA Also, since ฮ” OMB โ‰… ฮ” OMA โˆด BM = AM โ‡’ BM = AM = 1/2 AB From (1) AM = 1/2AB 2AM = AB AB = 2AM Putting value of AM AB = 2 ร— โˆš3/2 ร— 21 AB = โˆš3 ร— 21 AB = 21โˆš3 Now, Area of ฮ” AOB = 1/2 ร— Base ร— Height = 1/2 ร— AB ร— OM = 1/2 ร— 21โˆš3 ร— 21/2 = (441โˆš3)/4 Area of the segment AYB = Area of sector โ€“ area of โˆ† ๐ด๐‘‚๐ต = (462 โ€“ 441/4 โˆš3 ) cm2

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