Multiple choice

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

  1. $45^{\circ}$
  2. $60^{\circ}$
  3. $75^{\circ}$
  4. $90^{\circ}$
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D Correct answer
Explanation

A square inscribed in a circle divides the circle into 4 equal arcs. Each side of the square subtends an angle of 360 / 4 = 90 degrees at the center.

AI explanation

A square has four equal sides, and when inscribed in a circle, its vertices divide the circumference into four equal arcs of 360 / 4 = 90 degrees each. The angle subtended by any side at the center of the circle corresponds to the central angle of its arc. Therefore, each side of the square subtends an angle of 90 degrees at the center.

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