An arc AB of a circle subtends an angle x radians at the centre o of the circle. Given that the area of
the sector AOB is equal to the square of the length of the arc AB, find the value of x.
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Step-by-step explanation:
AB is a chord to the circle with center O and radius r. Arc AB subtends an angle x radian at the center. Draw OM ⏊ AB such that AM=BM
⎳AOB=x rad
OA = OB = r
Area of sector AOB = (arc AB)² —-(1)
Arc length of AB = rx
Area of sector AOB = (1/2) r² x
From (1),
(1/2) r² x = (rx)²
x² = x/2
x²-(x/2) = 0
x =0 or x = 1/2
Neglecting trivial solution x=0,
x = 1/2
Ans: Value of x = 0.5
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