question_answer

In the given figure above, O is the centre of the circle, If \[OA=3cm,AC=3cm\] and OX is perpendicular to AC, \[\angle \mathbf{ABC}\] is equal to?

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

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

C)  \[{{30}^{{}^\circ }}\]  

D)  None of these

Correct Answer: C

Solution :

(c):    Given, \[OA=3\]cm. and \[AC=3\]cm \[\Rightarrow \]  \[AM=\frac{1}{2}cm\] \[sin\theta =\frac{AM}{OA}=\frac{3/2}{3}\] \[\Rightarrow \]\[sin\theta =\frac{1}{2}\Rightarrow \theta ={{30}^{{}^\circ }}\] \[\angle AOC=2\theta ={{60}^{{}^\circ }}\] By using the property of circle. \[\angle ABC=\frac{1}{2}\angle AOC\] \[=\frac{{{60}^{{}^\circ }}}{2}={{30}^{{}^\circ }}\]