(Prove) 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.

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.

x=4

step-by-step explanation: