Short Introduction
Exercise 5.5 focuses on finding the length of a chord when the radius and the perpendicular distance from the centre are known. Students also derive a general formula for the length of a chord and understand how the distance from the centre affects the length of a chord.
Quick Information Box
| Particular | Details |
|---|---|
| Class | 9 |
| Subject | Mathematics |
| Chapter | 5 – I’m Up and Down, and Round and Round |
| Exercise | 5.5 |
| Main Topic | Length of Chords |
| Difficulty Level | Moderate |
| Important Concepts | Pythagoras Theorem, Radius, Chords |
Concepts Used (Topics Covered)
- Perpendicular from Centre to Chord
- Midpoint of a Chord
- Baudhāyana–Pythagoras Theorem
- Formula for Chord Length
- Relationship between Chord and Distance from Centre
Important Formulas
1. Pythagoras Theorem
2. Half Chord Formula
3. Chord Length Formula
Exercise 5.5 Solutions
Question 1
Find the length of the chord of a circle where the radius is 7 cm and perpendicular distance is 6 cm.
Solution
Question 2
Explain why the following statement is true:
Solution
Question 3 (*)
In a circle, if the distance of chord AB from the centre is twice the distance of another chord CD from the centre, then can we conclude that
[CD=2AB?]
Give reasons.
Solution
Common Mistakes
❌ Forgetting that the perpendicular from the centre bisects the chord.
❌ Using the entire chord instead of half-chord in Pythagoras Theorem.
❌ Assuming chord length is directly proportional to distance from the centre.
❌ Squaring numbers incorrectly.
Exam Tips
✔ Always draw a figure before solving.
✔ Use half of the chord in right-angled triangles.
✔ Remember: longer chords are nearer to the centre.
Practice MCQs
1. Radius = 13 cm and distance from centre = 5 cm. Find the chord length.
A. 10 cm
B. 12 cm
C. 24 cm
D. 26 cm
Answer:
Answer: C
2. The longest chord of a circle is:
A. Radius
B. Diameter
C. Arc
D. Tangent
Answer: B
3. A chord nearer to the centre is:
A. Shorter
B. Equal
C. Longer
D. Cannot be determined
Answer: C
4. The perpendicular from the centre to a chord:
A. Bisects the chord
B. Doubles the chord
C. Is parallel to the chord
D. None of these
Answer: A
Frequently Asked Questions (FAQs)
Q1. Which theorem is used in Exercise 5.5?
Baudhāyana–Pythagoras Theorem.
Q2. Why is only half of the chord used in calculations?
Because the perpendicular from the centre bisects the chord.
Q3. Which is the greatest chord of a circle?
The diameter.
Q4. Does a greater distance from the centre mean a longer chord?
No. Greater distance means a shorter chord.
Key Takeaways
✅ Chord Length Formula:
✅ Longer chords lie closer to the centre.
✅ Diameter is the greatest chord.
✅ Pythagoras Theorem is extremely useful in circle geometry.
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