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Two chords AB,CD of lengths 5 cm , 11cm respectively of a circle are parallel. If the distance between AB and CD is 3cm find the radius of the circle I'm unable to get correct answer of this problem please help?
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Two chords AB,CD of lengths 5 cm , 11cm respectively of a circle are p...
(2.5)^2+x^2=(5.5)+(3-x)^2 ...
find x = ? . ..
then,Radius=r=sq.Rt (2.5^2+x^2) ... ..
find x = ? . ..
then,Radius=r=sq.Rt (2.5^2+x^2) ... ..
Community Answer
Two chords AB,CD of lengths 5 cm , 11cm respectively of a circle are p...
Solution:
Let's consider a circle with center O and radius r.
Let AB and CD be the two parallel chords of lengths 5 cm and 11 cm respectively.
The distance between AB and CD is given as 3 cm.
Key Information:
- Chords AB and CD are parallel.
- The distance between AB and CD is 3 cm.
Step 1: Draw a Diagram
To visualize the problem, draw a circle with center O and radius r.
Draw two parallel chords AB and CD within the circle, such that the distance between AB and CD is 3 cm.
Step 2: Connect the Chords to the Center
Draw radii OA and OC, where A and C are the midpoints of AB and CD respectively.
Step 3: Analyze the Triangle
We have formed a triangle OAC with sides OA, AC, and OC.
Step 4: Use Pythagorean Theorem
As the chords are parallel, the distance between them is constant throughout. This means that triangles OAB and OCD are similar.
Using the Pythagorean theorem, we can find the length of OC:
OC^2 = OA^2 + AC^2
Step 5: Breaking Down the Lengths
We know that AC is the distance between AB and CD, which is 3 cm.
Since A and C are midpoints, OA and OC are perpendicular bisectors of AB and CD respectively.
Therefore, AO = BO = 5/2 cm and CO = DO = 11/2 cm.
Substituting the values, we have:
OC^2 = (5/2)^2 + 3^2
Step 6: Simplify and Solve
OC^2 = 25/4 + 9
OC^2 = 34/4
OC^2 = 17/2
Taking the square root of both sides, we get:
OC = √(17/2)
Therefore, the radius of the circle is √(17/2) cm.
Final Answer:
The radius of the circle is approximately 2.92 cm.
Let's consider a circle with center O and radius r.
Let AB and CD be the two parallel chords of lengths 5 cm and 11 cm respectively.
The distance between AB and CD is given as 3 cm.
Key Information:
- Chords AB and CD are parallel.
- The distance between AB and CD is 3 cm.
Step 1: Draw a Diagram
To visualize the problem, draw a circle with center O and radius r.
Draw two parallel chords AB and CD within the circle, such that the distance between AB and CD is 3 cm.
Step 2: Connect the Chords to the Center
Draw radii OA and OC, where A and C are the midpoints of AB and CD respectively.
Step 3: Analyze the Triangle
We have formed a triangle OAC with sides OA, AC, and OC.
Step 4: Use Pythagorean Theorem
As the chords are parallel, the distance between them is constant throughout. This means that triangles OAB and OCD are similar.
Using the Pythagorean theorem, we can find the length of OC:
OC^2 = OA^2 + AC^2
Step 5: Breaking Down the Lengths
We know that AC is the distance between AB and CD, which is 3 cm.
Since A and C are midpoints, OA and OC are perpendicular bisectors of AB and CD respectively.
Therefore, AO = BO = 5/2 cm and CO = DO = 11/2 cm.
Substituting the values, we have:
OC^2 = (5/2)^2 + 3^2
Step 6: Simplify and Solve
OC^2 = 25/4 + 9
OC^2 = 34/4
OC^2 = 17/2
Taking the square root of both sides, we get:
OC = √(17/2)
Therefore, the radius of the circle is √(17/2) cm.
Final Answer:
The radius of the circle is approximately 2.92 cm.
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Two chords AB,CD of lengths 5 cm , 11cm respectively of a circle are parallel. If the distance between AB and CD is 3cm find the radius of the circle I'm unable to get correct answer of this problem please help?
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Two chords AB,CD of lengths 5 cm , 11cm respectively of a circle are parallel. If the distance between AB and CD is 3cm find the radius of the circle I'm unable to get correct answer of this problem please help? 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 Two chords AB,CD of lengths 5 cm , 11cm respectively of a circle are parallel. If the distance between AB and CD is 3cm find the radius of the circle I'm unable to get correct answer of this problem please help? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two chords AB,CD of lengths 5 cm , 11cm respectively of a circle are parallel. If the distance between AB and CD is 3cm find the radius of the circle I'm unable to get correct answer of this problem please help?.
Two chords AB,CD of lengths 5 cm , 11cm respectively of a circle are parallel. If the distance between AB and CD is 3cm find the radius of the circle I'm unable to get correct answer of this problem please help? 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 Two chords AB,CD of lengths 5 cm , 11cm respectively of a circle are parallel. If the distance between AB and CD is 3cm find the radius of the circle I'm unable to get correct answer of this problem please help? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two chords AB,CD of lengths 5 cm , 11cm respectively of a circle are parallel. If the distance between AB and CD is 3cm find the radius of the circle I'm unable to get correct answer of this problem please help?.
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