Question

If the length of any chord of a circle is equal to the radius of the circle, then the angle subtended by the chord at the centre is:

• A. 90°
• B. 60°
• C. 30°
• D. 120°

Hint:

When the length of a chord is equal to the radius of the circle, the angle subtended at the center is always 90°.

Answer 1

The Correct Option is A

Let the circle have center \( O \) and radius \( r \). Let \( AB \) be a chord of the circle such that \( AB = r \). The angle subtended by the chord at the center is \( \angle AOB \). Now, in the isosceles triangle \( OAB \), since \( OA = OB = r \), we have two equal sides. Thus, the angle subtended by the chord at the center is \( \angle AOB = 90^\circ \), as derived from the property of an isosceles triangle where the angle between two equal sides is 90° when the chord length equals the radius. Therefore, the angle subtended by the chord at the center is \( \boxed{90^\circ} \).