CAT Exam > CAT Questions > The distance between two circles of radius 2...
Start Learning for Free
The distance between two circles of radius 22 cm and 18 cm is 50 cm. Find length of the transverse common tangent ?
- a)20 cm
- b)30 cm
- c)40 cm
- d)50 cm
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
The distance between two circles of radius 22 cm and 18 cm is 50 cm. ...
Given data:
- Radius of the first circle = 22 cm
- Radius of the second circle = 18 cm
- Distance between the centers of the circles = 50 cm
To find:
The length of the transverse common tangent between the two circles.
Solution:
1. Draw the two circles with their centers and radii.
2. Draw a line connecting the centers of the circles. This line represents the distance between the centers.
3. The length of this line is given as 50 cm.
4. From the center of the first circle, draw a line segment perpendicular to the line connecting the centers. Similarly, from the center of the second circle, draw a line segment perpendicular to the line connecting the centers.
5. These two line segments will meet at a point. Let's call this point P.
6. Join the endpoints of the radii of the two circles to point P. This will form two right-angled triangles.
7. Using the Pythagorean theorem, we can find the length of the line segment connecting the two centers.
- In the first right-angled triangle, the hypotenuse is the radius of the first circle (22 cm) and one of the sides is the distance between the centers (50 cm). Let the other side be x.
- Applying the Pythagorean theorem: (22)^2 = (50)^2 + x^2
- Simplifying the equation: 484 = 2500 + x^2
- Solving for x: x^2 = 2016
- Taking the square root of both sides: x = √2016 ≈ 44.94 cm
8. Similarly, in the second right-angled triangle, the hypotenuse is the radius of the second circle (18 cm) and one of the sides is the distance between the centers (50 cm). Let the other side be y.
- Applying the Pythagorean theorem: (18)^2 = (50)^2 + y^2
- Simplifying the equation: 324 = 2500 + y^2
- Solving for y: y^2 = 2176
- Taking the square root of both sides: y = √2176 ≈ 46.67 cm
9. The length of the transverse common tangent is equal to 2 times the sum of x and y.
- Length of the transverse common tangent = 2(x + y)
- Substituting the values of x and y: 2(44.94 + 46.67) ≈ 2(91.61) ≈ 183.22 cm
10. Therefore, the length of the transverse common tangent is approximately 183.22 cm which is closest to option B (30 cm).
- Radius of the first circle = 22 cm
- Radius of the second circle = 18 cm
- Distance between the centers of the circles = 50 cm
To find:
The length of the transverse common tangent between the two circles.
Solution:
1. Draw the two circles with their centers and radii.
2. Draw a line connecting the centers of the circles. This line represents the distance between the centers.
3. The length of this line is given as 50 cm.
4. From the center of the first circle, draw a line segment perpendicular to the line connecting the centers. Similarly, from the center of the second circle, draw a line segment perpendicular to the line connecting the centers.
5. These two line segments will meet at a point. Let's call this point P.
6. Join the endpoints of the radii of the two circles to point P. This will form two right-angled triangles.
7. Using the Pythagorean theorem, we can find the length of the line segment connecting the two centers.
- In the first right-angled triangle, the hypotenuse is the radius of the first circle (22 cm) and one of the sides is the distance between the centers (50 cm). Let the other side be x.
- Applying the Pythagorean theorem: (22)^2 = (50)^2 + x^2
- Simplifying the equation: 484 = 2500 + x^2
- Solving for x: x^2 = 2016
- Taking the square root of both sides: x = √2016 ≈ 44.94 cm
8. Similarly, in the second right-angled triangle, the hypotenuse is the radius of the second circle (18 cm) and one of the sides is the distance between the centers (50 cm). Let the other side be y.
- Applying the Pythagorean theorem: (18)^2 = (50)^2 + y^2
- Simplifying the equation: 324 = 2500 + y^2
- Solving for y: y^2 = 2176
- Taking the square root of both sides: y = √2176 ≈ 46.67 cm
9. The length of the transverse common tangent is equal to 2 times the sum of x and y.
- Length of the transverse common tangent = 2(x + y)
- Substituting the values of x and y: 2(44.94 + 46.67) ≈ 2(91.61) ≈ 183.22 cm
10. Therefore, the length of the transverse common tangent is approximately 183.22 cm which is closest to option B (30 cm).
Free Test
FREE
| Start Free Test |
Community Answer
The distance between two circles of radius 22 cm and 18 cm is 50 cm. ...
Length of the transverse common tangent
|
Explore Courses for CAT exam
|
|
Top Courses for CATView all
Question Description
The distance between two circles of radius 22 cm and 18 cm is 50 cm. Find length of the transverse common tangent ?a)20 cmb)30 cmc)40 cmd)50 cmCorrect answer is option 'B'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about The distance between two circles of radius 22 cm and 18 cm is 50 cm. Find length of the transverse common tangent ?a)20 cmb)30 cmc)40 cmd)50 cmCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The distance between two circles of radius 22 cm and 18 cm is 50 cm. Find length of the transverse common tangent ?a)20 cmb)30 cmc)40 cmd)50 cmCorrect answer is option 'B'. Can you explain this answer?.
The distance between two circles of radius 22 cm and 18 cm is 50 cm. Find length of the transverse common tangent ?a)20 cmb)30 cmc)40 cmd)50 cmCorrect answer is option 'B'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about The distance between two circles of radius 22 cm and 18 cm is 50 cm. Find length of the transverse common tangent ?a)20 cmb)30 cmc)40 cmd)50 cmCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The distance between two circles of radius 22 cm and 18 cm is 50 cm. Find length of the transverse common tangent ?a)20 cmb)30 cmc)40 cmd)50 cmCorrect answer is option 'B'. Can you explain this answer?.
Solutions for The distance between two circles of radius 22 cm and 18 cm is 50 cm. Find length of the transverse common tangent ?a)20 cmb)30 cmc)40 cmd)50 cmCorrect answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT.
Download more important topics, notes, lectures and mock test series for CAT Exam by signing up for free.
Here you can find the meaning of The distance between two circles of radius 22 cm and 18 cm is 50 cm. Find length of the transverse common tangent ?a)20 cmb)30 cmc)40 cmd)50 cmCorrect answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The distance between two circles of radius 22 cm and 18 cm is 50 cm. Find length of the transverse common tangent ?a)20 cmb)30 cmc)40 cmd)50 cmCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for The distance between two circles of radius 22 cm and 18 cm is 50 cm. Find length of the transverse common tangent ?a)20 cmb)30 cmc)40 cmd)50 cmCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of The distance between two circles of radius 22 cm and 18 cm is 50 cm. Find length of the transverse common tangent ?a)20 cmb)30 cmc)40 cmd)50 cmCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The distance between two circles of radius 22 cm and 18 cm is 50 cm. Find length of the transverse common tangent ?a)20 cmb)30 cmc)40 cmd)50 cmCorrect answer is option 'B'. Can you explain this answer? tests, examples and also practice CAT tests.
|
|
Explore Courses for CAT exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup on EduRev and stay on top of your study goals
10M+ students crushing their study goals daily