Mathematics
A and B are points on a circle with center O. C is a point on the circle such that OC bisects ∠AOB, prove that OC bisects the arc AB.
Circles
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Answer
The figure of the circle is shown below:
Given,
OC bisects ∠AOB.
∴ ∠AOC = ∠BOC
Since, equal arcs subtend equal angles at center.
∴ AC = BC
∴ C is mid-point of AB.
Hence, proved that OC bisects the arc AB.
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