Prove that in same segment angle subtended at centre is double angle subtended at circle.
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Theorem: The angle subtended by an arc of a circle at its centre is twice of the angle it subtends anywhere on the circle's circumference. The proof of this theorem is quite simple, and uses the exterior angle theorem – an exterior angle of a triangle is equal to the sum of the opposite interior angles.
Explanation:
Theorem: The angle subtended by an arc of a circle at its centre is twice of the angle it subtends anywhere on the circle's circumference. The proof of this theorem is quite simple, and uses the exterior angle theorem – an exterior angle of a triangle is equal to the sum of the opposite interior angles.
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