the figure shows a unit circle with Centre O and AB AC are tangents. If angle A is equal to 60 degree find the area of the quadrilateral ABCD.
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Given : a unit circle with Centre O
AB and AC are tangents
∠A = 60°
To Find : Area of Quadrilateral ABOC
Solution:
Area of Quadrilateral ABOC = Area of ΔOBA + area of ΔOCA
ΔOBA
∠B = 90°
∠A = 60°/2 = 30°
=> tan30° = OB/AB
OB = 1 ( unit circle)
=> 1/√3 = 1/AB
=> AB = √3
Area of ΔOBA = (1/2) (OB) * AB
= (1/2) * 1 * √3
area of ΔOCA = Area of ΔOBA
=> Area of Quadrilateral ABOC = √3/2 + √3/2
= √3 sq units
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