Since OA and OB are radii, triangle AOB is isosceles. Given ∠AOB = 60°, the other two angles are also 60°. Thus, triangle AOB is equilateral, so AB = OA = 12 cm.
In a circle with centre O, the central angle AOB is 60°. If the radius of the circle is 12 cm, what is the length of the chord AB?
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OA and OB are radii of the circle, so OA = OB = 12 cm. Therefore, triangle AOB is isosceles. Since ∠AOB = 60°, the remaining two angles together are 120° and each is 60°. Hence, triangle AOB is an equilateral triangle. All its sides are equal. Therefore, AB = OA = OB = 12 cm. So, the length of chord AB is 12 cm.
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