Multiple choice

What is the length of the chord of a unit circle which subtends an angle 2θ at the centre, where θ < 45°?

  1. sin 2θ

  2. cos 2θ

  3. 2 sinθ

  4. 2 cosθ
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C Correct answer
Explanation

In a unit circle, a chord subtending angle 2*theta at the center forms an isosceles triangle with two radii of length 1. Dropping a perpendicular from the center to the chord bisects the angle into theta and the chord into two segments of length sin(theta). Thus, the total length is 2 * sin(theta).

AI explanation

A perpendicular drawn from the centre of the circle to the chord bisects both the chord and the central angle 2*theta, creating a right triangle with hypotenuse 1 and angle theta. Using the sine ratio for this right triangle, sin(theta) equals half the chord length divided by 1. Multiplying by 2 gives the full chord length as 2 sin(theta). The result is 2 sin*theta*.

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