In a circle with center O, AC is a chord. OB is perpendicular to AC, and B is the midpoint of AC. If the angle ∠AOC = 120°, and the radius of the circle is 10 cm, what is the length of the chord AC?
Show answer & explanation
Correct answer: D
Explanation
Given:
Radius (r) = 10 cm
∠AOC = 120°
Formula:
Length of chord = 2r sin(θ/2)
AC = 2 × 10 × sin(120°/2)
AC = 20 × sin60°
AC = 20 × (√3/2)
AC = 10√3
Chord AC = 10√3 cm