question_answer

A square ABCD is inscribed in a circle with centre 0. Then the angle subtended by each side of the square at the centre O is

A) \[{{120}^{o}}\]                                  

B) \[{{180}^{o}}\]

C) \[{{45}^{o}}\]            

D)        \[{{90}^{o}}\]  

Correct Answer: D

Solution :

A square has four equal sides. \[\therefore \]Each side subtends the same angle at the centre\[O\]. Let angle subtended be\[{{x}^{o}}\]. So,       \[4{{x}^{o}}={{360}^{o}}\] \[\Rightarrow \]   \[{{x}^{o}}=\frac{{{360}^{o}}}{4}={{90}^{o}}\]