QQuestion
Prove that in any circle, angles in the same segment are equal.
✓Answer
Given: Let ∠ACB and ∠ADB be any two angles in the segment ABDC of a circle with centre O.
To prove: All angles in the same segment ABDC of the circle are equal.
Construction: O, A and O, B are joined.
Proof:
The angle ∠AOB is at the centre; the angles ∠ACB and ∠ADB on the circle are on the same arc APB.
Therefore,
∴ ∠AOB = 2∠ACB
and ∠AOB = 2∠ADB
Hence,
2∠ACB = 2∠ADB
∴ ∠ACB = ∠ADB
Therefore, angles in the same segment of a circle are equal.
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