Equal Chords and Their Distances from the CentrePractice Questions & MCQs
Practice Equal Chords and Their Distances from the Centre questions from Circles (Class 9 Maths) - important MCQs with answers and step-by-step solutions. Solve the sample questions below, then practice the full set free on the RankByte app.
Equal Chords and Their Distances from the CentreQuiz - Solve & Score
Q1. A circle of radius 13 cm has one chord 5 cm from the centre and another 12 cm from the centre. The chord nearer the centre is longer; by how many cm does the longer chord exceed the shorter?
- A.14 cm
- B.24 cm
- C.7 cm
- D.10 cm
Answer: A. 14 cm
Reading the problem, 13 cm, 5 cm, 12 cm (math, chapter 'Circles'). What we must find: how many cm does the longer chord exceed the shorter?. From the chapter we use the relation: Nearer chord (distance 5) = 2×.√.(13^2-5^2) = 24. The arithmetic is: Nearer chord (distance 5) = 2×.√.(13^2-5^2) = 24 → farther = 10 → difference = 24 - 10 = 14 cm. That lands on option A) 14 cm. As for the others, option B) '24 cm' doesn't hold - That is the longer chord itself; the question wants the DIFFERENCE; option C) '7 cm' fails since Find each chord by Pythagoras, then subtract the lengths.
Q2. A circle of radius 17 cm has one chord 8 cm from the centre and another 15 cm from the centre. The chord nearer the centre is longer; by how many cm does the longer chord exceed the shorter?
- A.14 cm
- B.30 cm
- C.7 cm
- D.16 cm
Answer: A. 14 cm
Reading the problem, 17 cm, 8 cm, 15 cm (math, chapter 'Circles'). The unknown we need is how many cm does the longer chord exceed the shorter?. The principle that connects these is - Nearer chord (distance 8) = 2×.√.(17^2-8^2) = 30. Putting the numbers in: Nearer chord (distance 8) = 2×.√.(17^2-8^2) = 30 → farther = 16 → difference = 30 - 16 = 14 cm. That lands on option A) 14 cm. As for the others, option B) '30 cm' fails since That is the longer chord itself; the question wants the DIFFERENCE; option C) '7 cm' is wrong because Find each chord by Pythagoras, then subtract the lengths.
Q3. Two equal chords of a circle of radius 5 cm are each 3 cm from the centre. For each chord, by how many cm does its length exceed its distance from the centre?
- A.5 cm
- B.8 cm
- C.1 cm
- D.2 cm
Answer: A. 5 cm
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Where can I practise Equal Chords and Their Distances from the Centre questions for Class 9 Maths?
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Are these Equal Chords and Their Distances from the Centre questions important for the exam?
Yes. These Equal Chords and Their Distances from the Centre important questions follow the Maths exam pattern (CBSE Boards, plus JEE and NEET foundation), so they help with both school and competitive prep.
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