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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