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

Example 3 - Chapter 12 Class 10 Areas related to Circles - Part 2
Example 3 - Chapter 12 Class 10 Areas related to Circles - Part 3
Example 3 - Chapter 12 Class 10 Areas related to Circles - Part 4
Example 3 - Chapter 12 Class 10 Areas related to Circles - Part 5

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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 ∠AOB = 120°. (Use π = 22/7 ). In a given circle, Radius (r) = 21 cm And, 𝜃 = 120° Area of segment AYB = Area of sector OAYB – Area of ΔOAB Area of sector OAYB = 𝜃/360×𝜋𝑟2 = 120/360×22/7×(21)2 = 1/3×22/7×21×21 = 22 × 21 = 462 cm2 Finding area of Δ AOB Area Δ AOB = 1/2 × Base × Height We draw OM ⊥ AB ∴ ∠ OMB = ∠ OMA = 90° In Δ OMA & Δ OMB ∠ OMA = ∠ OMB OA = OB OM = OM ∴ Δ OMA ≅ Δ OMB ⇒ ∠ AOM = ∠ BOM ∴ ∠ AOM = ∠ BOM = 1/2 ∠ BOA Also, since Δ OMB ≅ Δ OMA ∴ BM = AM ⇒ BM = AM = 1/2 AB From (1) AM = 1/2AB 2AM = AB AB = 2AM Putting value of AM AB = 2 × √3/2 × 21 AB = √3 × 21 AB = 21√3 Now, Area of Δ AOB = 1/2 × Base × Height = 1/2 × AB × OM = 1/2 × 21√3 × 21/2 = (441√3)/4 Area of the segment AYB = Area of sector – area of ∆ 𝐴𝑂𝐵 = (462 – 441/4 √3 ) cm2

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.