Page 2 - Activity 2 Angle formed at center by an arc Ch.10 Circle

5. A piece of a circumference of circle between two points is called an arc.

6. Angle Subtended by an Arc of a Circle
Let we have a circle with centre at O and AB be its arc. Here, ∠AOB is the angle
subtended by arc AB ( ) at the centre of the circle.

Also, ∠APS is the angle subtended by arc AB ( ) at a point P on the remaining
part of the
circle.
7. Important Points about Angle Subtended by an Arc
1. The angle subtended by an arc at the centre is double the angle subtended by it
at any point on the remaining part of the circle.
2. Angles in the same segment of a circle are equal.
3. Angle in a semi-circle is a right angle.
4. If a line segment joining two points subtends equal angles at two other points
lying on the same side of the line containing the line segment, the four points lie
on a circle (i.e. they are concyclic).

Procedure