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Two circles of radii 5cm and 3cm intersect at two points and the distance between their centres is 4cm.Find the length of common chord.?
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Two circles of radii 5cm and 3cm intersect at two points and the dista...
Understanding the Problem
To find the length of the common chord between two intersecting circles, we need to apply some geometric principles. The given circles have the following properties:
- Radius of Circle 1 (R1) = 5 cm
- Radius of Circle 2 (R2) = 3 cm
- Distance between their centers (d) = 4 cm
Finding the Length of the Common Chord
1. Identify the Key Components:
- Let O1 and O2 be the centers of Circle 1 and Circle 2, respectively.
- Let P be the midpoint of the common chord.
- The lengths from each center to the midpoint (OP) can be derived using the Pythagorean theorem.
2. Calculate OP:
- The distance from O1 to P (x1) can be found using the formula:
x1 = sqrt(R1^2 - (d/2)^2)
- The distance from O2 to P (x2) is:
x2 = sqrt(R2^2 - (d/2)^2)
3. Determine d/2:
- Since d = 4 cm, we have d/2 = 2 cm.
4. Calculate x1 and x2:
- For Circle 1:
x1 = sqrt(5^2 - 2^2) = sqrt(25 - 4) = sqrt(21)
- For Circle 2:
x2 = sqrt(3^2 - 2^2) = sqrt(9 - 4) = sqrt(5)
5. Find Length of the Common Chord:
- The length of the common chord (L) can be calculated as:
L = 2 * sqrt(R1^2 - (d/2)^2)
6. Final Calculation:
- L = 2 * sqrt(25 - 4) = 2 * sqrt(21) ≈ 9.165 cm
Conclusion
The length of the common chord between the two intersecting circles is approximately 9.165 cm.
To find the length of the common chord between two intersecting circles, we need to apply some geometric principles. The given circles have the following properties:
- Radius of Circle 1 (R1) = 5 cm
- Radius of Circle 2 (R2) = 3 cm
- Distance between their centers (d) = 4 cm
Finding the Length of the Common Chord
1. Identify the Key Components:
- Let O1 and O2 be the centers of Circle 1 and Circle 2, respectively.
- Let P be the midpoint of the common chord.
- The lengths from each center to the midpoint (OP) can be derived using the Pythagorean theorem.
2. Calculate OP:
- The distance from O1 to P (x1) can be found using the formula:
x1 = sqrt(R1^2 - (d/2)^2)
- The distance from O2 to P (x2) is:
x2 = sqrt(R2^2 - (d/2)^2)
3. Determine d/2:
- Since d = 4 cm, we have d/2 = 2 cm.
4. Calculate x1 and x2:
- For Circle 1:
x1 = sqrt(5^2 - 2^2) = sqrt(25 - 4) = sqrt(21)
- For Circle 2:
x2 = sqrt(3^2 - 2^2) = sqrt(9 - 4) = sqrt(5)
5. Find Length of the Common Chord:
- The length of the common chord (L) can be calculated as:
L = 2 * sqrt(R1^2 - (d/2)^2)
6. Final Calculation:
- L = 2 * sqrt(25 - 4) = 2 * sqrt(21) ≈ 9.165 cm
Conclusion
The length of the common chord between the two intersecting circles is approximately 9.165 cm.
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Two circles of radii 5cm and 3cm intersect at two points and the distance between their centres is 4cm.Find the length of common chord.?
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Two circles of radii 5cm and 3cm intersect at two points and the distance between their centres is 4cm.Find the length of common chord.? 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 circles of radii 5cm and 3cm intersect at two points and the distance between their centres is 4cm.Find the length of common chord.? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two circles of radii 5cm and 3cm intersect at two points and the distance between their centres is 4cm.Find the length of common chord.?.
Two circles of radii 5cm and 3cm intersect at two points and the distance between their centres is 4cm.Find the length of common chord.? 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 circles of radii 5cm and 3cm intersect at two points and the distance between their centres is 4cm.Find the length of common chord.? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two circles of radii 5cm and 3cm intersect at two points and the distance between their centres is 4cm.Find the length of common chord.?.
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