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Consider the five points comprising of the vertices of a square and the intersection point of its diagonals. How many triangles can be formed using these points?
  • a)
    4
  • b)
    6
  • c)
    8
  • d)
    10
  • e)
    9
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
Consider the five points comprising of the vertices of a square and t...
Triangle Formation using the Points of a Square

To solve this problem, let's consider the given points: the four vertices of a square (A, B, C, and D) and the intersection point of its diagonals (O). We need to determine the number of triangles that can be formed using these points.

Identification of Triangles
To find the number of triangles, we need to identify all the possible combinations of three points among the given points. Since a triangle is formed by connecting three non-collinear points, we can select any three points from the given five points to form a triangle.

Forming Triangles
Let's consider all the possible combinations of three points from the given five points:

1. Triangle formed with A, B, and C.
2. Triangle formed with A, B, and D.
3. Triangle formed with A, B, and O.
4. Triangle formed with A, C, and D.
5. Triangle formed with A, C, and O.
6. Triangle formed with A, D, and O.
7. Triangle formed with B, C, and D.
8. Triangle formed with B, C, and O.
9. Triangle formed with B, D, and O.
10. Triangle formed with C, D, and O.

Counting the Triangles
From the above combinations, we can see that a total of 10 triangles can be formed using the given points. Therefore, the correct answer is option 'C' - 8.

Conclusion
In this problem, we considered the vertices of a square and the intersection point of its diagonals. By identifying all the possible combinations of three points, we determined that a total of 10 triangles can be formed using these points.
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Community Answer
Consider the five points comprising of the vertices of a square and t...
We can form a triangle by choosing 3 points out of 5
Total triangles = 5C3 = 10
But in this, 3 points are collinear in the cases of the 2 diagonals and must be excluded.
So, total triangles = 10 -2 = 8.
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Directions for Questions: The figure below shows the street map for a certain region with the street intersections marked from a through l. A person standing at an intersection can see along straight lines to other intersections that are in her line of sight and all other people standing at these intersections. For example, a person standing at intersection g can see all people standing at intersections b, c, e, f, h, and k. In particular, the person standing at intersection g can see the person standing at intersection e irrespective of whether there is a person standing at intersection f.Six people U, V, W, X, Y, and Z, are standing at different intersections. No two people are standing at the same intersection.The following additional facts are known.1. X, U, and Z are standing at the three corners of a triangle formed by three street segments.2. X can see only U and Z.3. Y can see only U and W.4. U sees V standing in the next intersection behind Z.5. W cannot see V or Z.6. No one among the six is standing at intersection d.(2019)Q. Who can V see?

The figure below shows the street map for a certain region with the street intersections marked from a through l. A person standing at an intersection can see along straight lines to other intersections that are in her line of sight and all other people standing at these intersections. For example, a person standing at intersection g can see all people standing at intersections b, c, e, f, h, and k. In particular, the person standing at intersection g can see the person standing at intersection e irrespective of whether there is a person standing at intersection f.Six people U, V, W, X, Y, and Z, are standing at different intersections. No two people are standing at the same intersection.The following additional facts are known. 1. X, U, and Z are standing at the three corners of a triangle formed by three street segments. 2. X can see only U and Z. 3. Y can see only U and W. 4. U sees V standing in the next intersection behind Z.5. W cannot see V or Z. 6. No one among the six is standing at intersection d.Q. Who is standing at intersection a?

InstructionsComprehension:The figure below shows the street map for a certain region with the street intersections marked from a through l. A person standing at an intersection can see along straight lines to other intersections that are in her line of sight and all other people standing at these intersections. For example, a person standing at intersection g can see all people standing at intersections b, c, e, f, h, and k. In particular, the person standing at intersection g can see the person standing at intersection e irrespective of whether there is a person standing at intersection f.Six people U, V, W, X, Y, and Z, are standing at different intersections. No two people are standing at the same intersection.The following additional facts are known.1. X, U, and Z are standing at the three corners of a triangle formed by three street segments.2. X can see only U and Z.3. Y can see only U and W.4. U sees V standing in the next intersection behind Z.5. W cannot see V or Z.6. No one among the six is standing at intersection d.Q.Who is standing at intersection a?

InstructionsComprehension:The figure below shows the street map for a certain region with the street intersections marked from a through l. A person standing at an intersection can see along straight lines to other intersections that are in her line of sight and all other people standing at these intersections. For example, a person standing at intersection g can see all people standing at intersections b, c, e, f, h, and k. In particular, the person standing at intersection g can see the person standing at intersection e irrespective of whether there is a person standing at intersection f.Six people U, V, W, X, Y, and Z, are standing at different intersections. No two people are standing at the same intersection.The following additional facts are known.1. X, U, and Z are standing at the three corners of a triangle formed by three street segments.2. X can see only U and Z.3. Y can see only U and W.4. U sees V standing in the next intersection behind Z.5. W cannot see V or Z.6. No one among the six is standing at intersection d.Q.Should a new person stand at intersection d, who among the six would she see?

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Consider the five points comprising of the vertices of a square and the intersection point of its diagonals. How many triangles can be formed using these points?a)4b)6c)8d)10e)9Correct answer is option 'C'. Can you explain this answer?
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