In an
In an ABCD square, n interior points are chosen on each side.
Find the number of all triangles whose vertices X, Y, and Z lie at these points and on different sides of the square.
Find the number of all triangles whose vertices X, Y, and Z lie at these points and on different sides of the square.
Correct answer:

Tips for related online calculators
You need to know the following knowledge to solve this word math problem:
We encourage you to watch this tutorial video on this math problem: video1
Related math problems and questions:
- N points on the side
An equilateral triangle A, B, and C on each of its inner sides lies N=13 points. Find the number of all triangles whose vertices lie at given points on different sides.
- Count of triangles
On each side of an ABCD square is 10 internal points. Determine the number of triangles with vertices at these points.
- Interior angles
In a quadrilateral ABCD, whose vertices lie on some circle, the angle at vertex A is 58 degrees, and the angle at vertex B is 134 degrees. Calculate the sizes of the remaining interior angles.
- Recursion squares
In the square, ABCD has inscribed a square so that its vertices lie at the centers of the sides of the square ABCD. The procedure of inscribing the square is repeated this way. The side length of the square ABCD is a = 22 cm. Calculate: a) the sum of peri
- Combi-triangle
Each square side is marked 10 different points outside the square's vertices. How many triangles can be constructed from this set of points, where each vertex of the triangle lies on the other side of the square?
- Diagonals 14073
There are three different points, C, E, and F, in the plane. Please draw the square ABCD when E and F lie on the diagonals of this square. How many solutions does the task have? Thank you
- Percentage 80164
I was given a square ABCD 4.2 cm. Find the set of all points that have a distance less than or equal to 2 cm from one of its vertices and lie inside this square. Indicate how much of the square this area occupies as a percentage.
- MO - triangles
On the AB and AC sides of the ABC triangle lies successive points E and F, and on segment EF lie point D. The EF and BC lines are parallel. It is true this ratio FD:DE = AE:EB = 2:1. The area of the ABC triangle is 27 hectares, and line segments EF, AD, a
- Candy - MO
Gretel deploys different numbers to the vertex of a regular octagon, from one to eight candy. Peter can then choose which three piles of candy to give Gretel others retain. The only requirement is that the three piles lie at the vertices of an isosceles t
- Circles
How many different circles are determined by 11 points at the plane if 7 of them lie in a straight line?
- Rectangle - parallelogram
A rectangle is circumscribed by a circle with a radius of 5 cm. The short side of the rectangle measures 6 cm. Calculate the perimeter of a parallelogram ABCD, whose vertices are the midpoints of the sides of the rectangle.
- CoG center
Find the position of the center of gravity of a system of four mass points having masses, m1, m2 = 2 m1, m3 = 3 m1, and m4 = 4 m1, if they lie at the vertices of an isosceles tetrahedron. (in all case
- Different 42191
How many different triangles with vertices formed by points A, B, C, D, E, and F can we create?
- Construct 30121
Point B is a vertex of rectangle ABCD. The diagonal BD of this rectangle lies on the line p. Point X is an interior point of side AD of rectangle ABCD, and point Y is an internal point of side CD. Construct the missing vertices D, A, and C of rectangle AB
- Hexagon - MO
The picture shows the ABCD square, the EFGD square, and the HIJD rectangle. Points J and G lie on the side CD and is true |DJ|
- Determined 3570
There are 12 points in space, with no three lying on a straight line. How many different planes are determined by these points?
- Points in plane
The plane is given 12 points, 5 of which are located on a straight line. How many different lines could be drawn from these points?