Question : AB is the chord of a circle such that AB = 10 cm. If the diameter of the circle is 20 cm, then the angle subtended by the chord at the centre is?
Option 1: $45^{\circ}$
Option 2: $60^{\circ}$
Option 3: $30^{\circ}$
Option 4: $90^{\circ}$
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Correct Answer: $60^{\circ}$
Solution :
Given: AB is the chord of a circle such that AB = 10 cm.
The diameter of the circle is 20 cm.
The line segment connecting any two points on the circle's circumference is known as the chord of a circle.
In $\triangle AOC$,
AO = 10 cm (radius)
⇒ AC = 5 cm
⇒ $\cos \theta =\frac{AC}{AO}$
⇒ $\cos \theta =\frac{5}{10}$
⇒ $\cos \theta =\frac{1}{2}=\cos 60^{\circ}$
⇒ $ \theta =60^{\circ}$
OA = OB (radius)
So, $\angle ABO = 60º$ and $\angle AOB = 60º$
Hence, the correct answer is $60^{\circ}$.
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