question_answer

The length of a chord of a circle is equal to the radius of the circle. The angle which this chord subtends on the longer segment of the circle is equal to

A) \[30{}^\circ \]  

B)                                        \[45{}^\circ \]

C) \[60{}^\circ \]

D)        \[90{}^\circ \]

Correct Answer: A

Solution :

  \[OA=OB=AB\] Hence \[\Delta \,\,OAB\] is equilateral so that \[\angle AOB={{60}^{o}}\]                 Hence the angle subtended by AB on the longer side of the circle                                                 \[=\frac{1}{2}\angle AOB={{30}^{o}}\]