BA and BC are two tangents drawn to a circle with Centre O and of unit radius from an external point P if they are both incline at an angle of 60 degree with each other find the area of shaded region
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Area of Shaded region =0.68 sq unit
Step-by-step explanation:
both Tangents inclined at an angle of 60° with each other
60°/2 = 30°
Tan 30° = OA/BA
OA = Radius = 1
=> 1/√3 = 1/BA
=> BA = √3
Area of Δ OBA = (1/2) OA * BA
= (1/2) * 1 * √3
Similarly area of OBA = (1/2) OC * BC
= (1/2) * 1 * √3
Area of OABC = √3 = 1.73
Sector angle = 120°
Area = (120/360)πr²
= (1/3) * (22/7) * 1²
= 22/21
= 1.05
Area of Shaded region = 1.73 - 1.05
= 0.68 sq unit
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