Problem:
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A Point in a Triangle

There is a triangle formed by three points $(x_1, y_1)$, $(x_2, y_2)$, $(x_3, y_3)$ on a plain.

Write a program which prints "YES" if a point $P$ $(x_p, y_p)$ is in the triangle and "NO" if not.

Input

Input consists of several datasets. Each dataset consists of:

$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$ $x_p$ $y_p$

All the input are real numbers. Input ends with EOF. The number of datasets is less than or equal to 100.

Constraints

You can assume that:

$ -100 \leq x_1, y_1, x_2, y_2, x_3, y_3, x_p, y_p \leq 100$

1.0 $\leq$ Length of each side of a tringle

0.001 $\leq$ Distance between $P$ and each side of a triangle

Output

For each dataset, print "YES" or "NO" in a line.

Sample Input

0.0 0.0 2.0 0.0 2.0 2.0 1.5 0.5
0.0 0.0 1.0 4.0 5.0 3.0 -1.0 3.0

Output for the Sample Input

YES
NO

Solution in JAVA (judge verdict: Accepted)

import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		Scanner scanner = new Scanner(System.in);
		double ax,ay,bx,by,cx,cy,px,py,sitaAB = 0,sitaBC = 0,sitaCA = 0;

		while(scanner.hasNext()){
			ax = scanner.nextDouble();
			ay = scanner.nextDouble();
			bx = scanner.nextDouble();
			by = scanner.nextDouble();
			cx = scanner.nextDouble();
			cy = scanner.nextDouble();
			px = scanner.nextDouble();
			py = scanner.nextDouble();

			sitaAB = Math.acos(prod(ax-px, ay-py, bx-px, by-py) / (range(ax, ay, px, py) * range(bx, by, px, py)));
			sitaBC = Math.acos(prod(bx-px, by-py, cx-px, cy-py) / (range(bx, by, px, py) * range(cx, cy, px, py)));
			sitaCA = Math.acos(prod(cx-px, cy-py, ax-px, ay-py) / (range(cx, cy, px, py) * range(ax, ay, px, py)));
			if(equal((sitaAB + sitaBC + sitaCA), Math.PI*2)){
				System.out.println("YES");
			}else{
				System.out.println("NO");
			}
		}
	}

	public static double prod(double x1, double y1, double x2, double y2){
		return ((x1*x2) + (y1*y2));
	}
	public static double range(double x1, double y1, double x2, double y2){
		return Math.sqrt(Math.pow(x2-x1, 2) + Math.pow(y2-y1, 2));
	}
	public static boolean equal(double a, double b){
		if((a-b) < 0.0000000001 && (a-b) > -0.0000000001){
			return true;
		}else{
			return false;
		}
	}
}