Mathematics

Prove that the angle subtended at the center of a circle is bisected by the radius passing through the mid-point of arc.

Circles

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Answer

The figure of the circle is shown below:

Prove that the angle subtended at the center of a circle is bisected by the radius passing through the mid-point of arc. Circle, ML Aggarwal Understanding Mathematics Solutions ICSE Class 9.

Let C be the mid-point of arc AB.

∴ AC = BC.

Since, equal arcs subtend equal angles at center.

∴ ∠AOC = ∠BOC.

Hence, proved that ∠AOC = ∠BOC.

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