Question : The radius of a circle is 10 cm. The angle made by chord AB at the centre of this circle is 60°. What is the length of this chord?
Option 1: 40 cm
Option 2: 20 cm
Option 3: 30 cm
Option 4: 10 cm
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Correct Answer: 10 cm
Solution :
Given, the radius of the circle = 10 cm
Angle made by chord AB at the centre of this circle = 60°
OA = OB = 10 cm
OAB is an isosceles triangle.
So, $\angle$OAB = $\angle$OAB = $\frac{180^\circ-60^\circ}{2}=60^\circ$ [by angle sum property.]
Since, $\angle$OAB = $\angle$OBA = $\angle$AOB = 60$^\circ$, OAB is an equilateral triangle.
So, OA = OB = AB = 10 cm
Hence, the correct answer is 10 cm.
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