Question

If the length of a chord of a circle is equal to its radius, then find the angle subtended by it at the minor arc of the circle

• A. 150
• B. 104
• C. 125
• D. 110

Answer 1

The correct option is A 150

GIven a circle with centre O and chord AB.OA=OB=AB=radius =r(say)
$\angle ACB$ is the angle subtended by chord AB at the minor arc.
$△AOB$ is clearly an equilateral triangle
$\Rightarrow \angle AOB={60}^{\circ }$
$\therefore Reflex\angle AOB={360}^{\circ }-{60}^{\circ }={300}^{\circ }$
$\therefore \angle ACB=\frac{1}{2}\times Reflex\angle AOB=\frac{1}{2}\times {300}^{\circ }={150}^{\circ }$