data/problems/102.yml
---
:id: 102
:name: Triangle containment
:url: https://projecteuler.net/problem=102
:content: "Three distinct points are plotted at random on a Cartesian plane, for which
-1000 ≤ _x_, _y_ ≤ 1000, such that a triangle is formed.\n\nConsider the following
two triangles:\n\nA(-340,495), B(-153,-910), C(835,-947) \n \nX(-175,41), Y(-421,-714),
Z(574,-645)\n\nIt can be verified that triangle ABC contains the origin, whereas
triangle XYZ does not.\n\nUsing [triangles.txt](project/resources/p102_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.\n\nNOTE: The first two examples in the file represent
the triangles in the example given above.\n\n"