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

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450

600

750

900

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answer is D.

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Detailed Solution

As we know, all sides of a square are equal. Hence, AB = BC = CD = DA. Now, the sides of the square represent chords of the circle. Therefore, all four sides of the inscribed square represent four equal chords of the circle.
As we know, there is a property of circles which states that if the chords of a circle are equal then they subtend an equal angle at the centre of the circle.
Hence, ∠AOB = ∠BOC = ∠COD = ∠DOA.
Finally, we know that the sum of angles around a point is equal to 3600.
Therefore, ∠AOB + ∠BOC + ∠COD + ∠DOA = 3600 ……...equation (1)
Let us assume that ∠AOB = x. Hence, all the angles will be equal to x,
∠AOB + ∠BOC + ∠COD + ∠DOA = 3600
Putting all value in equation (1), we get,
x + x + x + x = 3600
⇒ 4x = 3600
Dividing both sides by 4,
x = 900
Hence, we can say that,
∠AOB = ∠BOC = ∠COD = ∠DOA = 900
Sides of square subtend 900 at centre O of circle.
So, the correct answer is “Option 4”.

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