An arc AB of a circle subtends an angle x radian at the centre O. If the area of the sector AOB is equal to half of the square of length of arc AB, then what is x equal to ?
- A. 1/4
- B. 1/2
- C. 1 ✓
- D. 2
Correct Answer: C. 1
Explanation
Area of the sector = \frac{1}{2}r^2x. Length of the arc = rx. Given \frac{1}{2}r^2x = \frac{1}{2}(rx)^2, dividing by \frac{1}{2}r^2 gives x = x^2. Since x \gt 0, x = 1.
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