Question

Ten points are marked on one side of △ABC. Another side of △ABC has 11 marked points and the third side has 12 marked points. None of the points are a vertex of the triangle. If any three non-collinear points can be the vertices of a new triangle, how many such triangles are possible?

Answer 1

There are 505 possible triangles that can be formed using the marked points on the sides of triangle ABC.

Step-by-step explanation:

To find the number of triangles that can be formed using the marked points on the sides of triangle ABC, we need to consider the possible combinations of three points.

For the first side with 10 marked points, there are 10 choose 3 combinations, which can be calculated as C(10,3) = 120.

Similarly, for the second side with 11 marked points, there are C(11,3) = 165 combinations, and for the third side with 12 marked points, there are C(12,3) = 220 combinations.

Adding the three combinations together, we get 120 + 165 + 220 = 505. Therefore, there are 505 possible triangles that can be formed using the marked points.