SSC
Sample Paper
SSC CHSL (10+2) Sample Test Paper-9
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. \[\therefore OA=OB=AB\]