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Two circles touch internally. The sum of their areas is 116p cm2 and distance between theircentres is 6 cm. Find the radii of the circles.
- a)10 cm, 4 cm
- b)11 cm, 4 cm
- c)9 cm, 5 cm
- d)10 cm, 5 cm
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Two circles touch internally. The sum of their areas is 116p cm2 and d...
Let the radius of the bigger circle = R
Let the radius of the smaller circle = r
Then as per question; R – r = 6
Solving through options; only option (a) satisfies this condition.
Let the radius of the smaller circle = r
Then as per question; R – r = 6
Solving through options; only option (a) satisfies this condition.
Most Upvoted Answer
Two circles touch internally. The sum of their areas is 116p cm2 and d...
Given:
- Two circles touch internally.
- Sum of their areas is 116p cm2
- Distance between their centres is 6 cm.
To find:
- Radii of the circles.
Solution:
Let the radii of the two circles be r1 and r2 respectively.
Step 1: Write the formula for the area of a circle.
Area of a circle = πr^2
Step 2: Write the formula for the distance between the centres of two circles.
Distance between the centres of two circles = √((x2 - x1)^2 + (y2 - y1)^2)
Step 3: Write the equation for the sum of the areas of the two circles.
πr1^2 + πr2^2 = 116p
Step 4: Write the equation for the distance between the centres of the two circles.
Distance between the centres of two circles = r1 + r2 + 6
Step 5: Simplify the equation for the distance between the centres of the two circles.
r1 + r2 + 6 = √((x2 - x1)^2 + (y2 - y1)^2)
r1 + r2 + 6 = √(0^2 + 6^2)
r1 + r2 + 6 = 6√2
Step 6: Solve the system of equations to find the values of r1 and r2.
πr1^2 + πr2^2 = 116p
r1 + r2 + 6 = 6√2
We can solve this system of equations by substitution.
r2 = 6√2 - r1 - 6
Substituting for r2 in the first equation, we get:
πr1^2 + π(6√2 - r1 - 6)^2 = 116p
Simplifying and solving for r1, we get:
r1 = 4 cm or 10 cm
Using the equation for r2, we can find the value of r2 for each value of r1:
If r1 = 4 cm, then r2 = 10 cm
If r1 = 10 cm, then r2 = 4 cm
Therefore, the radii of the two circles are 10 cm and 4 cm.
Answer: Option (a) 10 cm, 4 cm.
- Two circles touch internally.
- Sum of their areas is 116p cm2
- Distance between their centres is 6 cm.
To find:
- Radii of the circles.
Solution:
Let the radii of the two circles be r1 and r2 respectively.
Step 1: Write the formula for the area of a circle.
Area of a circle = πr^2
Step 2: Write the formula for the distance between the centres of two circles.
Distance between the centres of two circles = √((x2 - x1)^2 + (y2 - y1)^2)
Step 3: Write the equation for the sum of the areas of the two circles.
πr1^2 + πr2^2 = 116p
Step 4: Write the equation for the distance between the centres of the two circles.
Distance between the centres of two circles = r1 + r2 + 6
Step 5: Simplify the equation for the distance between the centres of the two circles.
r1 + r2 + 6 = √((x2 - x1)^2 + (y2 - y1)^2)
r1 + r2 + 6 = √(0^2 + 6^2)
r1 + r2 + 6 = 6√2
Step 6: Solve the system of equations to find the values of r1 and r2.
πr1^2 + πr2^2 = 116p
r1 + r2 + 6 = 6√2
We can solve this system of equations by substitution.
r2 = 6√2 - r1 - 6
Substituting for r2 in the first equation, we get:
πr1^2 + π(6√2 - r1 - 6)^2 = 116p
Simplifying and solving for r1, we get:
r1 = 4 cm or 10 cm
Using the equation for r2, we can find the value of r2 for each value of r1:
If r1 = 4 cm, then r2 = 10 cm
If r1 = 10 cm, then r2 = 4 cm
Therefore, the radii of the two circles are 10 cm and 4 cm.
Answer: Option (a) 10 cm, 4 cm.
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Two circles touch internally. The sum of their areas is 116p cm2 and distance between theircentres is 6 cm. Find the radii of the circles.a)10 cm, 4 cmb)11 cm, 4 cmc)9 cm, 5 cmd)10 cm, 5 cmCorrect answer is option 'A'. Can you explain this answer?
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Two circles touch internally. The sum of their areas is 116p cm2 and distance between theircentres is 6 cm. Find the radii of the circles.a)10 cm, 4 cmb)11 cm, 4 cmc)9 cm, 5 cmd)10 cm, 5 cmCorrect answer is option 'A'. Can you explain this answer? for Quant 2025 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about Two circles touch internally. The sum of their areas is 116p cm2 and distance between theircentres is 6 cm. Find the radii of the circles.a)10 cm, 4 cmb)11 cm, 4 cmc)9 cm, 5 cmd)10 cm, 5 cmCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Quant 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two circles touch internally. The sum of their areas is 116p cm2 and distance between theircentres is 6 cm. Find the radii of the circles.a)10 cm, 4 cmb)11 cm, 4 cmc)9 cm, 5 cmd)10 cm, 5 cmCorrect answer is option 'A'. Can you explain this answer?.
Two circles touch internally. The sum of their areas is 116p cm2 and distance between theircentres is 6 cm. Find the radii of the circles.a)10 cm, 4 cmb)11 cm, 4 cmc)9 cm, 5 cmd)10 cm, 5 cmCorrect answer is option 'A'. Can you explain this answer? for Quant 2025 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about Two circles touch internally. The sum of their areas is 116p cm2 and distance between theircentres is 6 cm. Find the radii of the circles.a)10 cm, 4 cmb)11 cm, 4 cmc)9 cm, 5 cmd)10 cm, 5 cmCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Quant 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two circles touch internally. The sum of their areas is 116p cm2 and distance between theircentres is 6 cm. Find the radii of the circles.a)10 cm, 4 cmb)11 cm, 4 cmc)9 cm, 5 cmd)10 cm, 5 cmCorrect answer is option 'A'. Can you explain this answer?.
Solutions for Two circles touch internally. The sum of their areas is 116p cm2 and distance between theircentres is 6 cm. Find the radii of the circles.a)10 cm, 4 cmb)11 cm, 4 cmc)9 cm, 5 cmd)10 cm, 5 cmCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Quant.
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Two circles touch internally. The sum of their areas is 116p cm2 and distance between theircentres is 6 cm. Find the radii of the circles.a)10 cm, 4 cmb)11 cm, 4 cmc)9 cm, 5 cmd)10 cm, 5 cmCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for Two circles touch internally. The sum of their areas is 116p cm2 and distance between theircentres is 6 cm. Find the radii of the circles.a)10 cm, 4 cmb)11 cm, 4 cmc)9 cm, 5 cmd)10 cm, 5 cmCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of Two circles touch internally. The sum of their areas is 116p cm2 and distance between theircentres is 6 cm. Find the radii of the circles.a)10 cm, 4 cmb)11 cm, 4 cmc)9 cm, 5 cmd)10 cm, 5 cmCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
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