Class 9 Exam > Class 9 Questions > The perpendicular distance of a chord 8 cm lo...
Start Learning for Free
The perpendicular distance of a chord 8 cm long from the centre of a circle of radius 5 cm is
- a)2 cm
- b)9 cm
- c)4 cm
- d)3 cm
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
The perpendicular distance of a chord 8 cm long from the centre of a c...
Consider a circle having center O with a chord. Let OA be the radius of the circle and AB be the chord. As given in the question, the radius of the circle is 5 cm and length of chord is 8 cm. Let the distance between the center of the circle and chord be OP. So, this can be shown diagrammatically as:
It is clear from the diagram that OP is perpendicular to AB. As OP is perpendicular to AB and passes through the center O, it will bisect the chord AB at P. Now the length of AP will be,
AP =1/2 × AB
AP =1/2 × AB
AP = 1/2 × 8
AP = 4 cm
Since, triangle OPA is a right-angle triangle, we can easily apply the Pythagoras theorem which can be stated as b2+p2 = h2 where b, p and h are base, perpendicular and hypotenuse of the respective triangle.
In ΔOPA,
Since, triangle OPA is a right-angle triangle, we can easily apply the Pythagoras theorem which can be stated as b2+p2 = h2 where b, p and h are base, perpendicular and hypotenuse of the respective triangle.
In ΔOPA,
AP2+OP2=AO2
OP2 = AO2 − AP2
OP2= 52−42
OP = 3 cm
Therefore, the distance of the chord AB from the center is 3 cm.
Therefore, the distance of the chord AB from the center is 3 cm.
Most Upvoted Answer
The perpendicular distance of a chord 8 cm long from the centre of a c...
Free Test
FREE
| Start Free Test |
Community Answer
The perpendicular distance of a chord 8 cm long from the centre of a c...
Understanding the Problem
To find the perpendicular distance of a chord from the center of a circle, we can use the properties of triangles formed by the radius and the chord.
Given Information
- Length of the chord (AB) = 8 cm
- Radius of the circle (r) = 5 cm
Visualizing the Geometry
1. Draw a circle with center O and a chord AB.
2. Draw the perpendicular from O to AB, meeting it at point M (midpoint of AB).
3. OM is the perpendicular distance we need to find.
Breaking Down the Triangle
- Since M is the midpoint of AB, AM = MB = 4 cm (half of the chord).
- In triangle OMA, we can apply the Pythagorean theorem:
- OM^2 + AM^2 = OA^2
Where:
- OA = radius = 5 cm
- AM = 4 cm
Applying the Pythagorean Theorem
- Substitute the values:
- OM^2 + (4 cm)^2 = (5 cm)^2
- OM^2 + 16 = 25
- OM^2 = 25 - 16
- OM^2 = 9
- OM = √9 = 3 cm
Conclusion
Thus, the perpendicular distance of the chord from the center of the circle is:
3 cm
The correct answer is option 'D'.
To find the perpendicular distance of a chord from the center of a circle, we can use the properties of triangles formed by the radius and the chord.
Given Information
- Length of the chord (AB) = 8 cm
- Radius of the circle (r) = 5 cm
Visualizing the Geometry
1. Draw a circle with center O and a chord AB.
2. Draw the perpendicular from O to AB, meeting it at point M (midpoint of AB).
3. OM is the perpendicular distance we need to find.
Breaking Down the Triangle
- Since M is the midpoint of AB, AM = MB = 4 cm (half of the chord).
- In triangle OMA, we can apply the Pythagorean theorem:
- OM^2 + AM^2 = OA^2
Where:
- OA = radius = 5 cm
- AM = 4 cm
Applying the Pythagorean Theorem
- Substitute the values:
- OM^2 + (4 cm)^2 = (5 cm)^2
- OM^2 + 16 = 25
- OM^2 = 25 - 16
- OM^2 = 9
- OM = √9 = 3 cm
Conclusion
Thus, the perpendicular distance of the chord from the center of the circle is:
3 cm
The correct answer is option 'D'.
|
Explore Courses for Class 9 exam
|
|
Top Courses for Class 9View all
Question Description
The perpendicular distance of a chord 8 cm long from the centre of a circle of radius 5 cm isa)2 cmb)9 cmc)4 cmd)3 cmCorrect answer is option 'D'. Can you explain this answer? for Class 9 2025 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about The perpendicular distance of a chord 8 cm long from the centre of a circle of radius 5 cm isa)2 cmb)9 cmc)4 cmd)3 cmCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 9 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The perpendicular distance of a chord 8 cm long from the centre of a circle of radius 5 cm isa)2 cmb)9 cmc)4 cmd)3 cmCorrect answer is option 'D'. Can you explain this answer?.
The perpendicular distance of a chord 8 cm long from the centre of a circle of radius 5 cm isa)2 cmb)9 cmc)4 cmd)3 cmCorrect answer is option 'D'. Can you explain this answer? for Class 9 2025 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about The perpendicular distance of a chord 8 cm long from the centre of a circle of radius 5 cm isa)2 cmb)9 cmc)4 cmd)3 cmCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 9 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The perpendicular distance of a chord 8 cm long from the centre of a circle of radius 5 cm isa)2 cmb)9 cmc)4 cmd)3 cmCorrect answer is option 'D'. Can you explain this answer?.
Solutions for The perpendicular distance of a chord 8 cm long from the centre of a circle of radius 5 cm isa)2 cmb)9 cmc)4 cmd)3 cmCorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 9.
Download more important topics, notes, lectures and mock test series for Class 9 Exam by signing up for free.
Here you can find the meaning of The perpendicular distance of a chord 8 cm long from the centre of a circle of radius 5 cm isa)2 cmb)9 cmc)4 cmd)3 cmCorrect answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The perpendicular distance of a chord 8 cm long from the centre of a circle of radius 5 cm isa)2 cmb)9 cmc)4 cmd)3 cmCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for The perpendicular distance of a chord 8 cm long from the centre of a circle of radius 5 cm isa)2 cmb)9 cmc)4 cmd)3 cmCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of The perpendicular distance of a chord 8 cm long from the centre of a circle of radius 5 cm isa)2 cmb)9 cmc)4 cmd)3 cmCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The perpendicular distance of a chord 8 cm long from the centre of a circle of radius 5 cm isa)2 cmb)9 cmc)4 cmd)3 cmCorrect answer is option 'D'. Can you explain this answer? tests, examples and also practice Class 9 tests.
|
|
Explore Courses for Class 9 exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup on EduRev and stay on top of your study goals
10M+ students crushing their study goals daily