Problem 448:
Given a point $M_{c}$, a point $G$ and a point $I$, construct the triangle ABC.

Construction: 
1. Using the point $M_{c}$ and the point $G$, construct a point $C$ (rule W01);
2. Using the point $M_{c}$ and the point $I$, construct a line $IM_{c}$ (rule W02);
3. Using the point $I$ and the point $C$, construct a line $s_{c}$ (rule W02);
4. Using the point $I$ and the point $M_{c}$, construct a circle $k_over(I,M_{c})$ (rule W09);
5. Using the point $C$ and the line $IM_{c}$, construct a line $CP`_{c}$ (rule W16);
6. Using the point $M_{c}$, the line $CP`_{c}$ and the point $C$, construct a line $h_{M_{c},-1/1}(CP`_{c})$ (rule W15);
7. Using the circle $k_over(I,M_{c})$ and the line $h_{M_{c},-1/1}(CP`_{c})$, construct a point $C_{fo}$ and a point $P_{c}$ (rule W04);
8. Using the point $P_{c}$ and the point $I$, construct a circle $k(I,P_{a})$ (rule W06);
9. Using the circle $k(I,P_{a})$, the point $M_{c}$ and the point $I$, construct a line $x3$ and a line $c$ (rule W12);
10. Using the point $M_{c}$ and the line $c$, construct a line $m_{c}$ (rule W10b);
11. Using the line $m_{c}$ and the line $s_{c}$, construct a point $N_{c}$ (rule W03);
12. Using the point $I$ and the point $N_{c}$, construct a circle $k(N_{c},B)$ (rule W06);
13. Using the circle $k(N_{c},B)$ and the line $c$, construct a point $B$ and a point $A$ (rule W04);
14. Using the point $A$ and the point $B$, construct a point $\_M_{c}$ (rule W01);
15. Using the point $C$ and the point $A$, construct a point $\_M_{b}$ (rule W01);
16. Using the point $B$ and the point $C$, construct a point $\_M_{a}$ (rule W01);
17. Using the point $A$ and the point $\_M_{a}$ construct the line $\_t_{a}$ (rule W02);
18. Using the point $B$ and the point $\_M_{b}$ construct the line $\_t_{b}$ (rule W02);
19. Using the line $\_t_{a}$ and the line $\_t_{b}$ construct the point $\_G$ (rule W03);
20. Using the point $A$ and the point $B$ construct the line $\_c$ (rule W02);
21. Using the point $B$ and the point $C$ construct the line $\_a$ (rule W02);
22. Using the point $A$ and the point $C$ construct the line $\_b$ (rule W02);
23. Using the point $B$, the point $A$ and the point $C$ and the line $\_c$ and the line $\_b$ construct the angle bisector $\_s_{a}$ (rule W17);
24. Using the point $C$, the point $B$ and the point $A$ and the line $\_a$ and the line $\_c$ construct the angle bisector $\_s_{b}$ (rule W17);
25. Using the line $\_s_{a}$ and the line $\_s_{b}$ construct the point $\_I$ (rule W03);

Statement:
Prove that the point $G$ is identical to the point $\_G$.

