Geometry and TrigonometryHardCentral angle when a chord equals the radius
Geometry and Trigonometry practice question
In a circle with centre O, points A and B lie on the circle and the chord AB has the same length as the radius. What is the measure, in degrees, of angle AOB?
Answer: 60
OA and OB are radii, and AB equals the radius too, so triangle AOB has three equal sides — it is equilateral. Every angle of an equilateral triangle is 60°, including angle AOB.
Common wrong answers
- If you answered 30
- 30° is half the answer; the triangle's angles are all 60°.
- If you answered 90
- 90° would make AB the hypotenuse of a right isosceles triangle, with AB = r√2, longer than the radius.
- If you answered 120
- 120° would make AB = r√3, longer than the radius.
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