UPSC Exam > UPSC Questions > There are 24 equally spaced points lying on t... Start Learning for Free
There are 24 equally spaced points lying on the circumference of a circle. What is the maximum number of equilateral triangles that can be drawn by taking sets of three points as the vertices?
- a)4
- b)6
- c)8
- d)12
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
There are 24 equally spaced points lying on the circumference of a cir...
Explanation:
To form an equilateral triangle, the three vertices must be equidistant from each other. For n points, the number of equilateral triangles that can be formed is given by the formula:
nC3 - 3n
where nC3 is the number of ways to choose 3 points from n points, and 3n is the number of equilateral triangles formed by taking each point as the center.
For 24 points, the number of equilateral triangles that can be formed is:
24C3 - 3*24 = 2024 - 72 = 1952
However, some of these triangles will be congruent, so we need to divide by the number of congruent triangles to get the maximum number of distinct equilateral triangles.
Each equilateral triangle can be uniquely identified by the position of its top vertex (i.e., the vertex opposite the base). There are 8 such positions, corresponding to the 8 equilateral triangles that can be formed using 3 adjacent points on the circle.
Therefore, the maximum number of distinct equilateral triangles that can be formed is:
1952/8 = 244
Answer: c) 8
To form an equilateral triangle, the three vertices must be equidistant from each other. For n points, the number of equilateral triangles that can be formed is given by the formula:
nC3 - 3n
where nC3 is the number of ways to choose 3 points from n points, and 3n is the number of equilateral triangles formed by taking each point as the center.
For 24 points, the number of equilateral triangles that can be formed is:
24C3 - 3*24 = 2024 - 72 = 1952
However, some of these triangles will be congruent, so we need to divide by the number of congruent triangles to get the maximum number of distinct equilateral triangles.
Each equilateral triangle can be uniquely identified by the position of its top vertex (i.e., the vertex opposite the base). There are 8 such positions, corresponding to the 8 equilateral triangles that can be formed using 3 adjacent points on the circle.
Therefore, the maximum number of distinct equilateral triangles that can be formed is:
1952/8 = 244
Answer: c) 8
Free Test
FREE
| Start Free Test |
Community Answer
There are 24 equally spaced points lying on the circumference of a cir...
8
 | Explore Courses for UPSC exam |  |
Top Courses for UPSCView all
Top Courses for UPSC
Question Description
There are 24 equally spaced points lying on the circumference of a circle. What is the maximum number of equilateral triangles that can be drawn by taking sets of three points as the vertices?a)4b)6c)8d)12Correct answer is option 'C'. Can you explain this answer? for UPSC 2026 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about There are 24 equally spaced points lying on the circumference of a circle. What is the maximum number of equilateral triangles that can be drawn by taking sets of three points as the vertices?a)4b)6c)8d)12Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for UPSC 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for There are 24 equally spaced points lying on the circumference of a circle. What is the maximum number of equilateral triangles that can be drawn by taking sets of three points as the vertices?a)4b)6c)8d)12Correct answer is option 'C'. Can you explain this answer?.
There are 24 equally spaced points lying on the circumference of a circle. What is the maximum number of equilateral triangles that can be drawn by taking sets of three points as the vertices?a)4b)6c)8d)12Correct answer is option 'C'. Can you explain this answer? for UPSC 2026 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about There are 24 equally spaced points lying on the circumference of a circle. What is the maximum number of equilateral triangles that can be drawn by taking sets of three points as the vertices?a)4b)6c)8d)12Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for UPSC 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for There are 24 equally spaced points lying on the circumference of a circle. What is the maximum number of equilateral triangles that can be drawn by taking sets of three points as the vertices?a)4b)6c)8d)12Correct answer is option 'C'. Can you explain this answer?.
Solutions for There are 24 equally spaced points lying on the circumference of a circle. What is the maximum number of equilateral triangles that can be drawn by taking sets of three points as the vertices?a)4b)6c)8d)12Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for UPSC. Download more important topics, notes, lectures and mock test series for UPSC Exam by signing up for free.
Here you can find the meaning of There are 24 equally spaced points lying on the circumference of a circle. What is the maximum number of equilateral triangles that can be drawn by taking sets of three points as the vertices?a)4b)6c)8d)12Correct answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of There are 24 equally spaced points lying on the circumference of a circle. What is the maximum number of equilateral triangles that can be drawn by taking sets of three points as the vertices?a)4b)6c)8d)12Correct answer is option 'C'. Can you explain this answer?, a detailed solution for There are 24 equally spaced points lying on the circumference of a circle. What is the maximum number of equilateral triangles that can be drawn by taking sets of three points as the vertices?a)4b)6c)8d)12Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of There are 24 equally spaced points lying on the circumference of a circle. What is the maximum number of equilateral triangles that can be drawn by taking sets of three points as the vertices?a)4b)6c)8d)12Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice There are 24 equally spaced points lying on the circumference of a circle. What is the maximum number of equilateral triangles that can be drawn by taking sets of three points as the vertices?a)4b)6c)8d)12Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice UPSC tests.
| Explore Courses for UPSC exam | |
Top Courses for UPSC
Explore Courses
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
