Question

From the given figure identify the following:
(a) Three radii
(b) A chord
(c) A sector
(d) A segment

Answer 1

Hint: We solve this problem by using the definitions of the required parameters.
(1) The radius of a circle is defined as the distance from the centre of a circle to the boundary of a circle.
(2) The chord of a circle is defined as a line segment that is formed by joining the two points on the circle.
(3) A sector is defined as a region formed by two radii along the arc formed from the radii of the circle. (4) A segment is defined as a region that is cut off from the circle by the chord
By using the above definitions we find the required parameters.

Complete step by step answer:
We are asked to find the required parameters from the given circle.
Let us go for one by one.
(a) Three radii
We know that the radius of a circle is defined as the distance from the centre of a circle to the boundary of a circle.
By using the definition we have three line segments that satisfy the definition of a radius.
So, we have the radii of the given figure as
\[\Rightarrow OA,OB,OC\]
Therefore the three radii are
\[\therefore OA,OB,OC\]
(b) A chord.
We know that the chord of a circle is defined as a line segment that is formed by joining the two points on the circle.
By using the definition of a chord we can see that there are two line segments that are formed by joining the two points on the circle they are \[ED,AC\]
Therefore, the chords of given figure are
\[\therefore ED,AC\]
(c) A sector
For finding the sector let us take the two more random points on the circle as shown below.

We know that a sector is defined as a region formed by two radii along the arc formed from the radii of the circle.
Now, by using the definition of a sector we have different sectors that are formed by two radii and arc of the radii they are
(1) \[OAYB\]
(2) \[OBC\]
(3) \[OAEDC\]
(4) \[OABC\]
Here, we can see that the above mentioned are all sectors.
(d) A segment

We know that a segment is defined as a region that is cut off from the circle by the chord
Now, by using the definition of a segment we have some segments from the figure they are
(1) \[EXD\]
(2) \[EABCD\]
(3) \[AEDC\]
(4) \[ABC\]
Here, we can say that the above mentioned are all segments.

Note: Students may miss some of the sectors and segments.
We have four sectors in the given figure they are
(1) \[OAYB\]
(2) \[OBC\]
(3) \[OAEDC\]
(4) \[OABC\]
These four are sectors of given figure. But students may miss two or more sectors because some of them are formed by the diameter. We need to keep in mind that the diameter is also a chord formed by two radii.
So, we can say that the regions that are formed by diameter also can become sectors and segments.