Class 9 Exam > Class 9 Questions > Given a circle of radius 5 cm and centre o . ...
Start Learning for Free
Given a circle of radius 5 cm and centre o . OL is drawn perpendicular to the chord AB . if OL=3 then find lenght of chord AB. freinds i dodnt find this answer could u help me finding it please
Most Upvoted Answer
Given a circle of radius 5 cm and centre o . OL is drawn perpendicular...
As when we draw the figure we can see that there is a right angle triangle-(LOB) Hence as OB is hypotenus,OL is perpendicular and LB is base then=>OB=5 cm ( radius )=>OL=3cm (given)Hence LB = 4 cm ( pythagorus theorum)Hence AB = (2×4) = 8cm.That's all.
Community Answer
Given a circle of radius 5 cm and centre o . OL is drawn perpendicular...
Problem:
Given a circle with a radius of 5 cm and center O. OL is drawn perpendicular to the chord AB. If OL = 3 cm, find the length of chord AB.
Solution:
To find the length of chord AB, we can use the properties of perpendiculars and chords in a circle. Let's break down the solution into smaller steps.
Step 1: Understand the Problem
We have a circle with a radius of 5 cm and center O. We are given that OL is perpendicular to chord AB, and OL has a length of 3 cm. We need to find the length of chord AB.
Step 2: Visualize the Problem
It is essential to have a clear visualization of the problem to solve it effectively. Draw a circle with center O and radius 5 cm. Draw a perpendicular line OL from the center O to chord AB. Label the length of OL as 3 cm.
Step 3: Identify Key Concepts
To solve the problem, we need to use the following key concepts:
1. Perpendicular from the center of a circle bisects the chord.
2. The length of the perpendicular from the center to a chord is the bisector of the chord.
Step 4: Apply Key Concepts
Since OL is perpendicular to chord AB, it bisects AB into two equal parts. Let's consider the two parts of AB as AO and BO. Since OL bisects AB, we have:
AO = BO
We know that OL = 3 cm, and the radius of the circle is 5 cm. Using the Pythagorean theorem, we can find the length of AO or BO.
Applying the Pythagorean theorem:
AO² + OL² = AL²
AO² + 3² = 5²
AO² + 9 = 25
AO² = 16
AO = 4 cm
Since AO = BO, the length of AB is the sum of AO and BO:
AB = AO + BO
AB = 4 cm + 4 cm
AB = 8 cm
Step 5: Final Answer
The length of chord AB is 8 cm.
Given a circle with a radius of 5 cm and center O. OL is drawn perpendicular to the chord AB. If OL = 3 cm, find the length of chord AB.
Solution:
To find the length of chord AB, we can use the properties of perpendiculars and chords in a circle. Let's break down the solution into smaller steps.
Step 1: Understand the Problem
We have a circle with a radius of 5 cm and center O. We are given that OL is perpendicular to chord AB, and OL has a length of 3 cm. We need to find the length of chord AB.
Step 2: Visualize the Problem
It is essential to have a clear visualization of the problem to solve it effectively. Draw a circle with center O and radius 5 cm. Draw a perpendicular line OL from the center O to chord AB. Label the length of OL as 3 cm.
Step 3: Identify Key Concepts
To solve the problem, we need to use the following key concepts:
1. Perpendicular from the center of a circle bisects the chord.
2. The length of the perpendicular from the center to a chord is the bisector of the chord.
Step 4: Apply Key Concepts
Since OL is perpendicular to chord AB, it bisects AB into two equal parts. Let's consider the two parts of AB as AO and BO. Since OL bisects AB, we have:
AO = BO
We know that OL = 3 cm, and the radius of the circle is 5 cm. Using the Pythagorean theorem, we can find the length of AO or BO.
Applying the Pythagorean theorem:
AO² + OL² = AL²
AO² + 3² = 5²
AO² + 9 = 25
AO² = 16
AO = 4 cm
Since AO = BO, the length of AB is the sum of AO and BO:
AB = AO + BO
AB = 4 cm + 4 cm
AB = 8 cm
Step 5: Final Answer
The length of chord AB is 8 cm.
Attention Class 9 Students!
To make sure you are not studying endlessly, EduRev has designed Class 9 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 9.
|
Explore Courses for Class 9 exam
|
|
Similar Class 9 Doubts
Top Courses for Class 9View all
Given a circle of radius 5 cm and centre o . OL is drawn perpendicular to the chord AB . if OL=3 then find lenght of chord AB. freinds i dodnt find this answer could u help me finding it please
Question Description
Given a circle of radius 5 cm and centre o . OL is drawn perpendicular to the chord AB . if OL=3 then find lenght of chord AB. freinds i dodnt find this answer could u help me finding it please for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Given a circle of radius 5 cm and centre o . OL is drawn perpendicular to the chord AB . if OL=3 then find lenght of chord AB. freinds i dodnt find this answer could u help me finding it please covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Given a circle of radius 5 cm and centre o . OL is drawn perpendicular to the chord AB . if OL=3 then find lenght of chord AB. freinds i dodnt find this answer could u help me finding it please .
Given a circle of radius 5 cm and centre o . OL is drawn perpendicular to the chord AB . if OL=3 then find lenght of chord AB. freinds i dodnt find this answer could u help me finding it please for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Given a circle of radius 5 cm and centre o . OL is drawn perpendicular to the chord AB . if OL=3 then find lenght of chord AB. freinds i dodnt find this answer could u help me finding it please covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Given a circle of radius 5 cm and centre o . OL is drawn perpendicular to the chord AB . if OL=3 then find lenght of chord AB. freinds i dodnt find this answer could u help me finding it please .
Solutions for Given a circle of radius 5 cm and centre o . OL is drawn perpendicular to the chord AB . if OL=3 then find lenght of chord AB. freinds i dodnt find this answer could u help me finding it please 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 Given a circle of radius 5 cm and centre o . OL is drawn perpendicular to the chord AB . if OL=3 then find lenght of chord AB. freinds i dodnt find this answer could u help me finding it please defined & explained in the simplest way possible. Besides giving the explanation of
Given a circle of radius 5 cm and centre o . OL is drawn perpendicular to the chord AB . if OL=3 then find lenght of chord AB. freinds i dodnt find this answer could u help me finding it please , a detailed solution for Given a circle of radius 5 cm and centre o . OL is drawn perpendicular to the chord AB . if OL=3 then find lenght of chord AB. freinds i dodnt find this answer could u help me finding it please has been provided alongside types of Given a circle of radius 5 cm and centre o . OL is drawn perpendicular to the chord AB . if OL=3 then find lenght of chord AB. freinds i dodnt find this answer could u help me finding it please theory, EduRev gives you an
ample number of questions to practice Given a circle of radius 5 cm and centre o . OL is drawn perpendicular to the chord AB . if OL=3 then find lenght of chord AB. freinds i dodnt find this answer could u help me finding it please tests, examples and also practice Class 9 tests.
|
|
Explore Courses for Class 9 exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup