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Answer:
The angle subtended by an arc at the center is double the angle subtended by it at any point on the remaining part of the circle.
Step-by-step explanation:
Let us consider the image attached.
Center of circle be O.
Arc AB subtends the angle on the circle and
on the center of the circle.
To prove:
Proof:
In : AO and PO are radius of the circles so AO = PO
And angles opposite to equal sides of a triangle are also equal in a triangle.
So,
Using external angle property, that external angle is equal to sum of two opposite internal angles of a triangle.
Similarly,
In : BO and PO are radius of the circles so BO = PO
And angles opposite to equal sides of a triangle are also equal in a triangle.
So,
Using external angle property, that external angle is equal to sum of two opposite internal angles of a triangle.
Now, we can see that:
Using equations (1) and (2):
Hence, proved.
