Go: package main

import (
	"bufio"
	"os"
	"strconv"
	"strings"
	"fmt"
)

var scanner = bufio.NewScanner(os.Stdin)

func main() {
	scanner.Scan()
	n, _ := strconv.Atoi(scanner.Text())
	for i := 0; i < n; i++ {
		scanner.Scan()
		input := strings.Split(scanner.Text(), " ")
		buf := make([]float64, len(input))
		for j := range buf {
			buf[j], _ = strconv.ParseFloat(input[j], 64)
		}
		p1 := complex(buf[0], buf[1])
		p2 := complex(buf[2], buf[3])
		p3 := complex(buf[4], buf[5])
		pk := complex(buf[6], buf[7])
		ps := complex(buf[8], buf[9])
		kin := isAtSameSide(p3, pk, []complex128{p1, p2}) &&
			isAtSameSide(p1, pk, []complex128{p2, p3}) &&
			isAtSameSide(p2, pk, []complex128{p3, p1})
		sin := isAtSameSide(p3, ps, []complex128{p1, p2}) &&
			isAtSameSide(p1, ps, []complex128{p2, p3}) &&
			isAtSameSide(p2, ps, []complex128{p3, p1})
		if (kin || sin) && !(kin && sin) {
			fmt.Println("OK")
		} else {
			fmt.Println("NG")
		}
	}
}

func isAtSameSide(a, b complex128, line []complex128) bool {
	sa := (real(line[1]) - real(line[0]))*(imag(a)-imag(line[0]))+
		(imag(line[1])-imag(line[0]))*(real(line[0])-real(a))
	sb := (real(line[1]) - real(line[0]))*(imag(b)-imag(line[0]))+
		(imag(line[1])-imag(line[0]))*(real(line[0])-real(b))
	return (sa > 0 && sb > 0) || (sa < 0 && sb < 0)
}

C++: #include<iostream>
#include<vector>
#include<complex>
#include<algorithm>
#include<cmath>
using namespace std;

#define EPS (1e-12)
#define EQ(a,b) (abs((a)-(b)) < EPS)
#define EQV(a,b) (EQ((a).real(),(b).real()) && EQ((a).imag(),(b).imag()))
typedef complex<double> Po;

Po unit(Po p){return p / abs(p);}
  
Po normal(Po p,int m){
  Po x;
  if(!m)x = p * Po(0,1);
  else x = p * Po(0,-1);
  return x;
}

double dot(Po x,Po y){return x.real()*y.real() + x.imag()*y.imag();}

double cross(Po x,Po y){return x.real()*y.imag() - x.imag()*y.real();}

double area(Po a,Po b,Po c){
  return abs(cross(b-a,c-a)/2);
}

bool inter(Po a,Po b,Po c,Po x){
  if( area(a,b,x) + area(b,c,x) + area(c,a,x) > area(a,b,c) +EPS)return false;
  else return true;
}

double heron(double a,double b,double c){
  double s = (a+b+c)/2;
  return sqrt(s*(s-a)*(s-b)*(s-c));
}

class line{
 public:
  Po a,b;

  void set(Po x,Po y){
    a = x;
    b = y;
  }

  bool orth(line l){
    return EQ( dot(a-b,l.a-l.b),0.0);
  }

  bool para(line l){
    return EQ( cross(a-b,l.a-l.b),0.0);
  }

  bool on_line(Po x){
    return EQ( cross(b-a,x-a),0.0);
  }

  double line_dis(Po x){
    return abs(cross(b-a,x-a))/abs(b-a);
  }

  Po line_cp(line l){
    return a + (b-a)*cross(l.b-l.a,l.a-a) /cross(l.b-l.a,b-a);
  }

  bool on_seg(Po x){
    return (abs(a-x) + abs(x-b) < abs(a-b) + EPS);
  }

  double seg_dis(Po x){
    if(dot(b-a,x-a)<EPS)return abs(x-a);
    if(dot(a-b,x-b)<EPS)return abs(x-b);
    return abs(cross(b-a,x-a))/abs(b-a);
  }

  int is_cross(line l){
    return (cross(b-a,l.a-a) * cross(b-a,l.b-a)<EPS) && (cross(l.b-l.a,a-l.a) * cross(l.b-l.a,b-l.a) < EPS);
  }

  Po seg_cp(line l){
    double d = abs(cross(l.b-l.a,a-l.a));
    return a + (b-a)*( d / (d * abs(cross(l.b-l.a,b-l.a))));
  }
};

class polygon{
 public:
  vector<Po> v;
  int o;

  void set(void){
    v.clear();
  }

  void Vadd(Po a){
    if(!v.size())o = 0;
    else if(a.imag() < v[o].imag())o = v.size();
    v.push_back(a);
  }

  void sort(void){
    vector<double> seta;
    Po ot;
    ot.real() = 1.0;
    ot.imag() = 0.0;
    swap(v[0],v[o]);
    o = 0;
    for(int i=1;i<(int)v.size();i++){
      seta.push_back(dot(ot,v[i]-v[0]) / (abs(ot)*abs(v[i]-v[0])) );
    } 
    for(int i=1;i<(int)v.size()-1;i++){
      for(int j=i+1;j<(int)v.size();j++){
	if(seta[i-1] < seta[j-1]){
	  swap(seta[i-1],seta[j-1]);
	  swap(v[i],v[j]);
	}
      }
    }
  }

  bool inter(Po a){
    int c = 0;
    double max = 0;
    Po b;
    line l,s;
    for(int i=0;i<(int)v.size();i++)if(max < v[i].real())max = v[i].real();
    b.real() = max+1;
    b.imag() = a.imag();
    s.set(a,b);
    for(int i=0;i<(int)v.size()-1;i++){
      l.set(v[i],v[i+1]);
      if(s.is_cross(l))c++;
    }
    l.set(v[(int)v.size()-1],v[0]);
    if(s.is_cross(l))c++;
    if(c%2)return true;
    else return false;
  }
};

int main(){
  int n;
  Po p1,p2,p3,pk,ps;
  polygon tri;

  cin >> n;

  for(int i=0;i<n;i++){
    cin >> p1.real() >> p1.imag();
    cin >> p2.real() >> p2.imag();
    cin >> p3.real() >> p3.imag();
    cin >> pk.real() >> pk.imag();
    cin >> ps.real() >> ps.imag();
    
    tri.set();
    tri.Vadd(p1);
    tri.Vadd(p2);
    tri.Vadd(p3);
    tri.sort();
    
    if(tri.inter(pk) != tri.inter(ps))cout << "OK" << endl;
    //if(inter(p1,p2,p3,pk) != inter(p1,p2,p3,ps) )cout << "OK" << endl;
    else cout << "NG" << endl;
  }
  
}

C++: #include <bits/stdc++.h>

using namespace std;

#define FST first
#define SND second

#define EPS (1e-5)

typedef complex<double> P;
typedef pair<P,P> SEG;

double cross(P a, P b) {
  return a.real()*b.imag()-a.imag()*b.real();
}

bool isIntersectSS(SEG a, SEG b) {
  return (cross(a.SND-a.FST, b.FST-a.FST) * cross(a.SND-a.FST, b.SND-a.FST) < EPS)
    && (cross(b.SND-b.FST, a.FST-b.FST) * cross(b.SND-b.FST, a.SND-b.FST) < EPS);
}

int main() {
  
  int N; cin >> N;
  
  while(N--) {
    P Wall[3];
    for(int i=0; i<3; i++) {
      double x, y; cin >> x >> y;
      Wall[i] = P(x, y);
    }
    
    double x, y;
    cin >> x >> y; P enemy(x, y);
    cin >> x >> y; P orihime(x, y);
    SEG seg(enemy, orihime);
    
    int ok = 0;
    for(int i=0; i<3; i++) {
      ok += isIntersectSS(seg, SEG(Wall[i], Wall[(i+1)%3]));
    }
    
    if(ok == 1) {
      cout << "OK" << endl;
    }
    else {
      cout << "NG" << endl;
    }
  }
  
  return 0;
}

C++: #include <cstdio>
#include <cstring>
#include <algorithm>
#include <string>
#include <cmath>
#include <stack>
#include <vector>
#include <map>
#include <set>
#include <queue>
#include <list>
#include <iostream>
#include <sstream>
#include <climits>
#include <cfloat>
#include <complex>


typedef long long ll;
const double Eps = 1e-6;


using namespace std;

typedef complex<double> Point;

double dot(const Point& a, const Point& b)
{
	return a.real()*b.real() + a.imag()*b.imag();
}
double cross(const Point& a, const Point& b)
{
	return a.real()*b.imag() - a.imag()*b.real();
}
double distance_line_point(const Point& a, const Point& b, const Point& point)
{
	return abs(cross(a-b, point-b) / abs(a-b));
}
double distance_linesegment_point(const Point& a, const Point& b, const Point& point)
{
	if (dot(b-a, point-a) < Eps)
		return abs(a-point);
	else if (dot(a-b, point-b) <Eps)
		return abs(b-point);
	else
		return distance_line_point(a, b, point);
}
bool is_in_triangle(const Point* triangle, const Point& point)
{
	double t[3];
	for (int i = 0; i < 3; ++i)
		t[i] = cross(triangle[(i+1)%3] - triangle[i], point - triangle[i]);

	return t[0] >= 0 && t[1] >= 0 && t[2] >= 0
		|| t[0] <= 0 && t[1] <= 0 && t[2] <= 0;
}
bool is_in_triangle(const Point& a, const Point& b, const Point& c, const Point& point)
{
	Point t[3] = { a, b, c };
	return is_in_triangle(t, point);
}

int main()
{
	int n;
	scanf("%d", &n);
	while (n--)
	{
		Point p[5];
		for (int i = 0; i < 5; ++i)
		{
			int a, b;
			scanf("%d %d", &a, &b);
			p[i] = Point(a, b);
		}

		if (is_in_triangle(p, p[3]) != is_in_triangle(p, p[4]))
			puts("OK");
		else
			puts("NG");
	}

	return 0;
}