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Chapter - 19

Angle Properties of A Circle

Theorem - 1. The angle subtended by an arc of a circle at the centre is double the angle subtended by it at any point on the remaining part of the circle.

Given : A circle with the centre O and an arc AB which subtend at any point C

To Prove :

Construction : CO is joined and produced to D

Proof :

Statement	Reason
1. OA = OB	1. Radii
2.	2. Statement (1)
3.	3. Ext.angle = sum of Int.opp.angles
4.	4. Statements (2) & (3)
5. Similarly	5. Statements (2) & (3)
6. In fig (i) and (iii)	6. Statement (4) and (5)
7. In fig (ii)	7. Statement (4) and (5)