Problem 102Published on Friday, 12th August 2005, 06:00 pm; Solved by 14015; Difficulty rating: 15%
Three distinct points are plotted at random on a Cartesian plane, for which -1000 ≤ x, y ≤ 1000, such that a triangle is formed.
Consider the following two triangles:
A(-340,495), B(-153,-910), C(835,-947)
X(-175,41), Y(-421,-714), Z(574,-645)
It can be verified that triangle ABC contains the origin, whereas triangle XYZ does not.
Using triangles.txt (right click and 'Save Link/Target As...'), a 27K text file containing the co-ordinates of one thousand "random" triangles, find the number of triangles for which the interior contains the origin.
NOTE: The first two examples in the file represent the triangles in the example given above.