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Find the area of the minor segment whose chord subtenda angle of measure 120° are redius of the circle is 42 cm

Asked by singhgaurav9537733089 2nd December 2018, 6:08 AM
Answered by Expert
Answer:
 
Figure shows the circle of radius 42 cm. Chord AB subtends 120° at centre O.
Area of the minor segment formed by the chord (shaded area in figure) is obtained by subtracting
area of ΔAOB from area of segment of the circle which subtends 120° at centre.
 
ΔAOC is a right angled triangle, whose angles are 90°, 60° and 30° .
since side opposite 90° is 42 cm, side opposite to 30° is 21 cm and side opposite to 60° is √3×21 = 36.4 cm
 
Area of minor segment = (1/3)π×42×42 - (1/2)×72.8×21 = 1083 cm
Answered by Expert 2nd December 2018, 9:44 AM
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