CBSE Class 9 Maths Lab Manual – Angles in the Same Segment

CBSE Class 9 Maths Lab Manual – Angles in the Same Segment

Objective
To show that the angles subtended by the chord of a circle in the same segment are equal, experimentally.

Prerequisite Knowledge

1. Concept of a circle.
2. Concept of angle subtended by an arc/chord.

Materials Required
Glazed papers, sketch pens, a pair of scissors, gluestick, geometry box, white sheet.

Procedure

1. Take red colour glazed paper and draw a circle of any radius say 2.5 cm on the white side of the paper.
2. Cut this circle with centre O and radius 2.5 cm.
3. Mark any point P on the circumference of the circle.
4. Mark two other points A and B on the circumference of the circle.
5. Fold and press the circle along AB to get a crease which is a chord of the circle.
6. Join PA and PB to get ∠APB as shown in fig. (i).
   
7. Take another coloured glazed paper say, yellow, cut circle of same radius.
8. Draw a chord CD on second circle with centre O’, such that AB = CD.
9. Mark a point R on the circumference of the second circle. Join RC and RD fig (ii).
   
10. Cut out ∆RCD and paste it on the first circle such that R lies on P and RD lies on PB and RC lies on PA as shown in fig. (iii).
    
    ∠APB superimposes ∠DRC

Observation
Since the chord AB = chord CD and ∠APB superimposes ∠DRC, their arcs are same. When two angles superimpose each other it means their two arms lie on one another. This verifies that angles in the same segments are equal.

Result
We verified that two angles subtended by the chord of a circle in the same segment are equal.

Learning Outcome
We learnt that two or more angles subtended by same chord in the same segment of a circle are equal.

Activity Time

1. This theorem can be verified by taking any point on the minor segment of circle.
2. Prove this theorem for different chords, such as diameter, chord in minor segment, chord in major segment.

Viva Voce

Question 1.
Define chord of a circle.
Answer:
A line segment AB joining two points A and B of the circle is called a chord of the circle.

Question 2.
How many longest chords are there in a circle ?
Answer:
There are infinity many longest chords in a circle passing through the centre.

Question 3.
Define minor segment of a circle.
Answer:
A chord divides a circle into two parts the smaller part is called as minor segment.

Question 4.
Define major segment of a circle.
Answer:
The larger part of the circle is called as major segment.

Question 5.
What is the measure of an angle formed in a semicircle ?
Answer:
90°

Question 6.
If the angle subtended by an arc at the centre is 30°, what is the value of angle subtended by it on the remaining part of the circle.
Answer:
15°

Question 7.
If the angle subtended by an arc at the centre in major segment is reflex angle, then what is the angle in the minor segment ?
Answer:
Obtuse angle.

Question 8.
The angle subtented by an arc at the circle in minor segment is obtuse angle. What is the values of angle subtended by it in the major segment ?
Answer:
Acute angle.

Multiple Choice Questions

Question 1.
Find ∠BDC, if ∠ABC = 70°, ∠ACB = 30°:

(i) 80°
(ii) 100°
(iii) 70°
(iv) none of these

Question 2.
If ∠BDC = 30°, find ∠BAC:

(i) 30°
(ii) 60°
(iii) 15°
(iv) none of these

Question 3.
In a circle with centre O, AB is a chord and P, Q, R are three points on the same side of the chord AB of circle. If ∠APB = 40°, what is value of ∠AQB, ∠ARB?
(i) 20°, 40°
(ii) 80°, 80°
(iii) 40°, 40°
(iv) none of these

Question 4.
Calculate the measure of ∠PQB, where O is the centre of the circle:

(i) 50°
(ii) 60°
(iii) 90°
(iv) none of these

Question 5.
If ∠PQS = 40°, ∠SPR = 65°, find ∠RSP.

(i) 70°
(ii) 75°
(iii) 105°
(iv) none of these

Question 6.
In the fig, ∠ABC = 69°, ∠ACB = 31°. Find ∠BDC:

(i) 80°
(ii) 100°
(iii) 70°
(iv) none of these

Question 7.
In the fig, ∠BEC = 130°, ∠ECD = 20°. Find ∠BAC:

(i) 50°
(ii) 110°
(iii) 70°
(iv) none of these

Question 8.
In a circle, ABCD is a cyclic quadrilateral in which ∠DBC = 80° and ∠BAC = 40°, find ∠DCB:

(i) 60°
(ii) 70°
(iii) 80°
(iv) none of these

Question 9.
In a circle, AB is a diameter, Q, P are any points on the circle. What is value of ∠AQB and ∠APB ?
(i) 80°, 90°
(ii) 90°, 90°
(iii) 50°, 50°
(iv) none of these

Answers

1. (i)
2. (i)
3. (iii)
4. (i)
5. (ii)
6. (i)
7. (ii)
8. (i)
9. (ii)

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