Question

A square in inscribed in a circle with centre O. What angle does each side subtend at centre O?

• A. ${45}^{\circ }$
• B. ${60}^{\circ }$
• C. ${75}^{\circ }$
• D. ${90}^{\circ }$

Answer 1

The correct option is D ${90}^{\circ }$

All sides of a square being equal, the angles subtend by each side at the centre are equal
$\Rightarrow \angle AOB=\angle BOC=\angle COD=\angle DOA=x\left(say\right)$
SInce, the sum of the angles round a point $={360}^{\circ }$
therefore,
$\Rightarrow \angle AOB+\angle BOC+\angle COD+\angle DOA={360}^{\circ }$
$\Rightarrow x+x+x+x={360}^{\circ }$
$\Rightarrow 4x={360}^{\circ }\Rightarrow x={90}^{\circ }$.