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Distance of chit AB from the center of a circle is 8 CM length of the chord AB is 12 CM find the diameter of the circle
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Distance of chit AB from the center of a circle is 8 CM length of the ...
Understanding the Problem
To find the diameter of the circle given the length of the chord AB and its distance from the center, we can apply some geometry principles.
Given Information
- Distance of chord AB from the center (d): 8 CM
- Length of chord AB (l): 12 CM
Visualization
Imagine a circle with center O and a chord AB. The perpendicular from point O to the midpoint M of the chord AB creates a right triangle OMA, where:
- OM = distance from the center to the chord (d)
- MA = half the length of the chord (l/2)
Calculating Half the Chord Length
- MA = 12 CM / 2 = 6 CM
Using the Right Triangle
In right triangle OMA, we can use the Pythagorean theorem:
- OA² = OM² + MA²
Here, OA represents the radius (r) of the circle.
Substituting Values
- r² = 8² + 6²
- r² = 64 + 36
- r² = 100
- r = √100 = 10 CM
Finding the Diameter
The diameter (D) of the circle is twice the radius:
- D = 2 * r
- D = 2 * 10 CM = 20 CM
Final Result
The diameter of the circle is 20 CM.
This method combines geometry and algebra to provide a clear solution to the problem, ensuring you understand each step in the process.
To find the diameter of the circle given the length of the chord AB and its distance from the center, we can apply some geometry principles.
Given Information
- Distance of chord AB from the center (d): 8 CM
- Length of chord AB (l): 12 CM
Visualization
Imagine a circle with center O and a chord AB. The perpendicular from point O to the midpoint M of the chord AB creates a right triangle OMA, where:
- OM = distance from the center to the chord (d)
- MA = half the length of the chord (l/2)
Calculating Half the Chord Length
- MA = 12 CM / 2 = 6 CM
Using the Right Triangle
In right triangle OMA, we can use the Pythagorean theorem:
- OA² = OM² + MA²
Here, OA represents the radius (r) of the circle.
Substituting Values
- r² = 8² + 6²
- r² = 64 + 36
- r² = 100
- r = √100 = 10 CM
Finding the Diameter
The diameter (D) of the circle is twice the radius:
- D = 2 * r
- D = 2 * 10 CM = 20 CM
Final Result
The diameter of the circle is 20 CM.
This method combines geometry and algebra to provide a clear solution to the problem, ensuring you understand each step in the process.
Community Answer
Distance of chit AB from the center of a circle is 8 CM length of the ...
20 cm
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Distance of chit AB from the center of a circle is 8 CM length of the chord AB is 12 CM find the diameter of the circle
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Distance of chit AB from the center of a circle is 8 CM length of the chord AB is 12 CM find the diameter of the circle 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 Distance of chit AB from the center of a circle is 8 CM length of the chord AB is 12 CM find the diameter of the circle covers all topics & solutions for Class 9 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Distance of chit AB from the center of a circle is 8 CM length of the chord AB is 12 CM find the diameter of the circle.
Distance of chit AB from the center of a circle is 8 CM length of the chord AB is 12 CM find the diameter of the circle 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 Distance of chit AB from the center of a circle is 8 CM length of the chord AB is 12 CM find the diameter of the circle covers all topics & solutions for Class 9 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Distance of chit AB from the center of a circle is 8 CM length of the chord AB is 12 CM find the diameter of the circle.
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