CAT Exam > CAT Questions > Let AB, CD, EF, GH, and JK be five diameters ...
Start Learning for Free
Let AB, CD, EF, GH, and JK be five diameters of a circle with center at O. In how many ways can three points be chosen out of A, B, C, D, E, F, G, H, J, K, and O so as to form a triangle?
Correct answer is '160'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
Let AB, CD, EF, GH, and JK be five diameters of a circle with center a...
There are 11 points from which a triangle can be formed. But there are 5 lines which have 3 points linearly.
Number of triangles formed = 11C3 – 5 (because of the lines)
165 – 5 = 160 triangles
Answer: 160
Most Upvoted Answer
Let AB, CD, EF, GH, and JK be five diameters of a circle with center a...
Understanding the problem:
We are given five diameters of a circle, namely AB, CD, EF, GH, and JK, with the center of the circle at O. We need to find the number of ways to choose three points from the set of points A, B, C, D, E, F, G, H, J, K, and O such that they form a triangle.
Approach:
To form a triangle, we need to choose three points that are not collinear. Let's analyze the possible cases to form a triangle.
Case 1: Choosing three points from one diameter:
- If we choose three points from one diameter, they will always be collinear and cannot form a triangle.
Case 2: Choosing two points from one diameter and the third point from a different diameter:
- We have five diameters, so there are 5 ways to choose the first point.
- Once the first point is chosen, we have four remaining points on the same diameter to choose the second point, giving us 4 ways.
- The third point can be chosen from the remaining eight points (excluding the two points already chosen), giving us 8 ways.
- Therefore, the total number of ways for this case is 5 * 4 * 8 = 160.
Case 3: Choosing all three points from different diameters:
- We have five diameters, so there are 5 ways to choose the first point.
- Once the first point is chosen, we have four remaining diameters to choose the second point from, giving us 4 ways.
- The third point can be chosen from the remaining eight points (excluding the two points already chosen), giving us 8 ways.
- Therefore, the total number of ways for this case is 5 * 4 * 8 = 160.
Total number of ways:
- Adding up the number of ways from Case 2 and Case 3, we get a total of 160 ways to choose three points to form a triangle.
Conclusion:
The correct answer is 160, as explained above.
We are given five diameters of a circle, namely AB, CD, EF, GH, and JK, with the center of the circle at O. We need to find the number of ways to choose three points from the set of points A, B, C, D, E, F, G, H, J, K, and O such that they form a triangle.
Approach:
To form a triangle, we need to choose three points that are not collinear. Let's analyze the possible cases to form a triangle.
Case 1: Choosing three points from one diameter:
- If we choose three points from one diameter, they will always be collinear and cannot form a triangle.
Case 2: Choosing two points from one diameter and the third point from a different diameter:
- We have five diameters, so there are 5 ways to choose the first point.
- Once the first point is chosen, we have four remaining points on the same diameter to choose the second point, giving us 4 ways.
- The third point can be chosen from the remaining eight points (excluding the two points already chosen), giving us 8 ways.
- Therefore, the total number of ways for this case is 5 * 4 * 8 = 160.
Case 3: Choosing all three points from different diameters:
- We have five diameters, so there are 5 ways to choose the first point.
- Once the first point is chosen, we have four remaining diameters to choose the second point from, giving us 4 ways.
- The third point can be chosen from the remaining eight points (excluding the two points already chosen), giving us 8 ways.
- Therefore, the total number of ways for this case is 5 * 4 * 8 = 160.
Total number of ways:
- Adding up the number of ways from Case 2 and Case 3, we get a total of 160 ways to choose three points to form a triangle.
Conclusion:
The correct answer is 160, as explained above.
Attention CAT Students!
To make sure you are not studying endlessly, EduRev has designed CAT study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in CAT.
|
Explore Courses for CAT exam
|
|
Similar CAT Doubts
Top Courses for CATView all
Let AB, CD, EF, GH, and JK be five diameters of a circle with center at O. In how many ways can three points be chosen out of A, B, C, D, E, F, G, H, J, K, and O so as to form a triangle?Correct answer is '160'. Can you explain this answer?
Question Description
Let AB, CD, EF, GH, and JK be five diameters of a circle with center at O. In how many ways can three points be chosen out of A, B, C, D, E, F, G, H, J, K, and O so as to form a triangle?Correct answer is '160'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Let AB, CD, EF, GH, and JK be five diameters of a circle with center at O. In how many ways can three points be chosen out of A, B, C, D, E, F, G, H, J, K, and O so as to form a triangle?Correct answer is '160'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let AB, CD, EF, GH, and JK be five diameters of a circle with center at O. In how many ways can three points be chosen out of A, B, C, D, E, F, G, H, J, K, and O so as to form a triangle?Correct answer is '160'. Can you explain this answer?.
Let AB, CD, EF, GH, and JK be five diameters of a circle with center at O. In how many ways can three points be chosen out of A, B, C, D, E, F, G, H, J, K, and O so as to form a triangle?Correct answer is '160'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Let AB, CD, EF, GH, and JK be five diameters of a circle with center at O. In how many ways can three points be chosen out of A, B, C, D, E, F, G, H, J, K, and O so as to form a triangle?Correct answer is '160'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let AB, CD, EF, GH, and JK be five diameters of a circle with center at O. In how many ways can three points be chosen out of A, B, C, D, E, F, G, H, J, K, and O so as to form a triangle?Correct answer is '160'. Can you explain this answer?.
Solutions for Let AB, CD, EF, GH, and JK be five diameters of a circle with center at O. In how many ways can three points be chosen out of A, B, C, D, E, F, G, H, J, K, and O so as to form a triangle?Correct answer is '160'. 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 Let AB, CD, EF, GH, and JK be five diameters of a circle with center at O. In how many ways can three points be chosen out of A, B, C, D, E, F, G, H, J, K, and O so as to form a triangle?Correct answer is '160'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Let AB, CD, EF, GH, and JK be five diameters of a circle with center at O. In how many ways can three points be chosen out of A, B, C, D, E, F, G, H, J, K, and O so as to form a triangle?Correct answer is '160'. Can you explain this answer?, a detailed solution for Let AB, CD, EF, GH, and JK be five diameters of a circle with center at O. In how many ways can three points be chosen out of A, B, C, D, E, F, G, H, J, K, and O so as to form a triangle?Correct answer is '160'. Can you explain this answer? has been provided alongside types of Let AB, CD, EF, GH, and JK be five diameters of a circle with center at O. In how many ways can three points be chosen out of A, B, C, D, E, F, G, H, J, K, and O so as to form a triangle?Correct answer is '160'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Let AB, CD, EF, GH, and JK be five diameters of a circle with center at O. In how many ways can three points be chosen out of A, B, C, D, E, F, G, H, J, K, and O so as to form a triangle?Correct answer is '160'. Can you explain this answer? tests, examples and also practice CAT tests.
|
|
Explore Courses for CAT exam
|
|
Suggested Free Tests
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 to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup