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Three circles touch each other externally. The distance between their centre is 5 cm, 6 cm and 7 cm. Find the radii of the circles :
- a)2 cm, 3 cm, 4 cm
- b)3 cm, 4 cm, 1 cm
- c)1 cm, 2.5 cm, 3.5 cm
- d)1 cm, 2 cm, 4 cm
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Three circles touch each other externally. The distance between their ...
Distance between the centre is 7 cm.
Radius of one circle (r1) = 4 cm
Radius of second circle (r2) = 7 - 4 = 3cm
just a example.
Most Upvoted Answer
Three circles touch each other externally. The distance between their ...
Given:
- Distance between the centers of the circles: 5 cm, 6 cm, and 7 cm
Explanation:
To find the radii of the circles, we need to consider the concept of externally touching circles. When three circles touch each other externally, the distance between their centers will be equal to the sum of their radii.
Calculation:
Let the radii of the circles be a, b, and c.
Given:
- Distance between the centers of the circles:
- 5 cm = a + b
- 6 cm = b + c
- 7 cm = c + a
Solving these equations simultaneously:
- Adding all three equations, we get:
- 5 + 6 + 7 = a + b + b + c + c + a
- 18 = 2(a + b + c)
- 9 = a + b + c
Since we are looking for radii a, b, and c, we can substitute the sum of the radii back into the equations to find the individual radii.
Final Answer:
- By solving for a, b, and c, we find that the radii of the circles are:
- a = 2 cm
- b = 3 cm
- c = 4 cm
Therefore, the correct answer is option A (2 cm, 3 cm, 4 cm).
- Distance between the centers of the circles: 5 cm, 6 cm, and 7 cm
Explanation:
To find the radii of the circles, we need to consider the concept of externally touching circles. When three circles touch each other externally, the distance between their centers will be equal to the sum of their radii.
Calculation:
Let the radii of the circles be a, b, and c.
Given:
- Distance between the centers of the circles:
- 5 cm = a + b
- 6 cm = b + c
- 7 cm = c + a
Solving these equations simultaneously:
- Adding all three equations, we get:
- 5 + 6 + 7 = a + b + b + c + c + a
- 18 = 2(a + b + c)
- 9 = a + b + c
Since we are looking for radii a, b, and c, we can substitute the sum of the radii back into the equations to find the individual radii.
Final Answer:
- By solving for a, b, and c, we find that the radii of the circles are:
- a = 2 cm
- b = 3 cm
- c = 4 cm
Therefore, the correct answer is option A (2 cm, 3 cm, 4 cm).
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Three circles touch each other externally. The distance between their centre is 5 cm, 6 cm and 7 cm. Find the radii of the circles :a)2 cm, 3 cm, 4 cmb)3 cm, 4 cm, 1 cmc)1 cm, 2.5 cm, 3.5 cmd)1 cm, 2 cm, 4 cmCorrect answer is option 'A'. Can you explain this answer?
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Three circles touch each other externally. The distance between their centre is 5 cm, 6 cm and 7 cm. Find the radii of the circles :a)2 cm, 3 cm, 4 cmb)3 cm, 4 cm, 1 cmc)1 cm, 2.5 cm, 3.5 cmd)1 cm, 2 cm, 4 cmCorrect answer is option 'A'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Three circles touch each other externally. The distance between their centre is 5 cm, 6 cm and 7 cm. Find the radii of the circles :a)2 cm, 3 cm, 4 cmb)3 cm, 4 cm, 1 cmc)1 cm, 2.5 cm, 3.5 cmd)1 cm, 2 cm, 4 cmCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three circles touch each other externally. The distance between their centre is 5 cm, 6 cm and 7 cm. Find the radii of the circles :a)2 cm, 3 cm, 4 cmb)3 cm, 4 cm, 1 cmc)1 cm, 2.5 cm, 3.5 cmd)1 cm, 2 cm, 4 cmCorrect answer is option 'A'. Can you explain this answer?.
Three circles touch each other externally. The distance between their centre is 5 cm, 6 cm and 7 cm. Find the radii of the circles :a)2 cm, 3 cm, 4 cmb)3 cm, 4 cm, 1 cmc)1 cm, 2.5 cm, 3.5 cmd)1 cm, 2 cm, 4 cmCorrect answer is option 'A'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Three circles touch each other externally. The distance between their centre is 5 cm, 6 cm and 7 cm. Find the radii of the circles :a)2 cm, 3 cm, 4 cmb)3 cm, 4 cm, 1 cmc)1 cm, 2.5 cm, 3.5 cmd)1 cm, 2 cm, 4 cmCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three circles touch each other externally. The distance between their centre is 5 cm, 6 cm and 7 cm. Find the radii of the circles :a)2 cm, 3 cm, 4 cmb)3 cm, 4 cm, 1 cmc)1 cm, 2.5 cm, 3.5 cmd)1 cm, 2 cm, 4 cmCorrect answer is option 'A'. Can you explain this answer?.
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Three circles touch each other externally. The distance between their centre is 5 cm, 6 cm and 7 cm. Find the radii of the circles :a)2 cm, 3 cm, 4 cmb)3 cm, 4 cm, 1 cmc)1 cm, 2.5 cm, 3.5 cmd)1 cm, 2 cm, 4 cmCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for Three circles touch each other externally. The distance between their centre is 5 cm, 6 cm and 7 cm. Find the radii of the circles :a)2 cm, 3 cm, 4 cmb)3 cm, 4 cm, 1 cmc)1 cm, 2.5 cm, 3.5 cmd)1 cm, 2 cm, 4 cmCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of Three circles touch each other externally. The distance between their centre is 5 cm, 6 cm and 7 cm. Find the radii of the circles :a)2 cm, 3 cm, 4 cmb)3 cm, 4 cm, 1 cmc)1 cm, 2.5 cm, 3.5 cmd)1 cm, 2 cm, 4 cmCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
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