Question : The diameter of a circle is 20 cm. The length of a chord AB is 10 cm. What will be the angle made by this chord at the centre of this circle?
Option 1: 75°
Option 2: 45°
Option 3: 60°
Option 4: 90°
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Correct Answer: 60°
Solution :
Radius = $\frac{\text{Diameter}}{2}$
In an equilateral triangle, since the three sides are equal the three angles opposite to the equal sides, are equal in measure.
OA = OB = AB = 10 cm
⇒ $\triangle$OAB is an equilateral triangle.
So, $\angle$OAB = $\angle$OBA = $\angle$AOB = $\frac{180}{3}$ = 60°,
Thus, the angle made by this chord at the centre of this circle = 60°
Hence, the correct answer is 60°.
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