## Problem:

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.

4613732

## Code:The solution may include methods that will be found here: Library.java .

public interface EulerSolution{public String run();}
/*  * Solution to Project Euler problem 2 * By Nayuki Minase *  * http://nayuki.eigenstate.org/page/project-euler-solutions * https://github.com/nayuki/Project-Euler-solutions */public final class p002 implements EulerSolution {		public static void main(String[] args) {		System.out.println(new p002().run());	}			public String run() {		int sum = 0;		for (int i = 0; ; i++) {			int fib = fibonacci(i);			if (fib > 4000000)				break;			if (fib % 2 == 0)				sum += fib;		}		return Integer.toString(sum);	}			private static int fibonacci(int x) {		if (x < 0 || x > 46)			throw new IllegalArgumentException();		int a = 0;		int b = 1;		for (int i = 0; i < x; i++) {			int c = a + b;			a = b;			b = c;		}		return a;	}	}

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