Problem 77:
Given a point $A$, a point $G$ and a point $I$, construct the triangle ABC.

Construction: 
1. Using the point $A$ and the point $G$, construct a point $M_{a}$ (rule W01);
2. Using the point $I$ and the point $M_{a}$, construct a line $IM_{a}$ (rule W02);
3. Using the point $I$ and the point $M_{a}$, construct a circle $k_over(I,M_{a})$ (rule W09);
4. Using the point $A$ and the line $IM_{a}$, construct a line $AP`_{a}$ (rule W16);
5. Using the point $M_{a}$, the line $AP`_{a}$ and the point $A$, construct a line $h_{M_{a},-1/1}(AP`_{a})$ (rule W15);
6. Using the circle $k_over(I,M_{a})$ and the line $h_{M_{a},-1/1}(AP`_{a})$, construct a point $A_{fo}$ and a point $P_{a}$ (rule W04);
7. Using the point $P_{a}$ and the point $I$, construct a circle $k(I,P_{a})$ (rule W06);
8. Using the circle $k(I,P_{a})$, the point $A$ and the point $I$, construct a line $c$ and a line $b$ (rule W12);
9. Using the circle $k(I,P_{a})$, the point $M_{a}$ and the point $I$, construct a line $x1$ and a line $a$ (rule W12);
10. Using the line $c$ and the line $a$, construct a point $B$ (rule W03);
11. Using the point $G$ and the point $B$, construct a point $M_{b}$ (rule W01);
12. Using the point $A$ and the point $M_{b}$, construct a point $C$ (rule W01);
13. Using the point $C$ and the point $A$, construct a point $\_M_{b}$ (rule W01);
14. Using the point $B$ and the point $C$, construct a point $\_M_{a}$ (rule W01);
15. Using the point $A$ and the point $\_M_{a}$ construct the line $\_t_{a}$ (rule W02);
16. Using the point $B$ and the point $\_M_{b}$ construct the line $\_t_{b}$ (rule W02);
17. Using the line $\_t_{a}$ and the line $\_t_{b}$ construct the point $\_G$ (rule W03);
18. Using the point $A$ and the point $B$ construct the line $\_c$ (rule W02);
19. Using the point $B$ and the point $C$ construct the line $\_a$ (rule W02);
20. Using the point $A$ and the point $C$ construct the line $\_b$ (rule W02);
21. 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);
22. 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);
23. Using the line $\_s_{a}$ and the line $\_s_{b}$ construct the point $\_I$ (rule W03);

Statement:
Prove that the point $I$ is identical to the point $\_I$.

