Page 4 - Activity 2 Angle formed at center by an arc Ch.10 Circle

Demonstration
Flere, ∠QOR = 2 ∠QPR
We find that the angle subtended by an arc at the centre is double the angle subtended
by it at any point on the remaining part of circle.

Observation
By actual measurement, ∠QOR = ………… ,
∠QPR = ………… ,
Therefore, ∠QOR = 2 ………… .

Result
We find that 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.

Application
The property is used in proving many other important results such as opposite angles of
a cyclic quadrilateral are always supplementary angles and angles in the same segment
of a circle are always equal.

Viva Voce
Question 1:
Define a circle.
Answer:
A circle is the collection of all points in a plane which are equidistant from a fixed point
within the same plane.

Question 2:
What is chord?
Answer:
A line segment which is formed by joining any two points on the circumference of circle.

Question 3:
How many circles can pass through three non-collinear points?
Answer:
There is only one such circle.

Question 4:
What is the diameter?
Answer:
The chord which passes through the centre of circle is known as the diameter of circle.

Question 5:
Which is the longest chord of circle?
Answer:
Diameter