question_answer

The angle subtended by a chord at its centre is \[60{}^\circ \]. then the ratio between chord and radius is

A) \[1:2\]                           

B) \[1:1\]

C) \[\sqrt{2}:1\]                 

D) \[2:1\]

Correct Answer: B

Solution :

  OA = OB = r units \[\angle \]AOC = \[30{}^\circ \]; AC = CB In \[\Delta \] AOC, sin \[AOC=\frac{AC}{OA}\] \[\Rightarrow \sin 30{}^\circ =\frac{AC}{r}\] \[\Rightarrow \frac{1}{2}=\frac{AC}{r}\] \[\Rightarrow AC=\frac{r}{2}\] \[\Rightarrow AB=2\times \frac{r}{2}=r\] units \[\therefore \] Required ratio \[=1:1\]                 \[\] OA = OB \[\therefore \angle OAB=\angle OBA=60{}^\circ \] \[\therefore \Delta \,OAB\] is an equilateral triangle. \[\therefore OA=OB=AB\]