Problem 493:
Given a point $G$, a point $H_{c}$ and a point $T_{c}$, construct the triangle ABC.

Construction: 
1. Using the point $H_{c}$ and the point $T_{c}$, construct a line $c$ (rule W02);
2. Using the point $H_{c}$ and the line $c$, construct a line $h_{c}$ (rule W10b);
3. Using the point $G$, the line $c$ and the point $H_{c}$, construct a line $h_{G,-2/1}(c)$ (rule W15);
4. Using the line $h_{G,-2/1}(c)$ and the line $h_{c}$, construct a point $C$ (rule W03);
5. Using the point $C$ and the point $G$, construct a point $M_{c}$ (rule W01);
6. Using the point $T_{c}$ and the point $C$, construct a line $s_{c}$ (rule W02);
7. Using the point $M_{c}$ and the line $c$, construct a line $m_{c}$ (rule W10b);
8. Using the line $m_{c}$ and the line $s_{c}$, construct a point $N_{c}$ (rule W03);
9. Using the point $C$ and the point $N_{c}$, construct a line $m(CN_{c})$ (rule W14);
10. Using the line $m(CN_{c})$ and the line $m_{c}$, construct a point $O$ (rule W03);
11. Using the point $C$ and the point $O$, construct a circle $k(O,C)$ (rule W06);
12. Using the circle $k(O,C)$ and the line $c$, construct a point $A$ and a point $B$ (rule W04);
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 $C$ and the line $\_c$ construct the line $\_h_{c}$ (rule W10b);
20. Using the line $\_c$ and the line $\_h_{c}$ construct the point $\_H_{c}$ (rule W03);
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 $A$, the point $C$ and the point $B$ and the line $\_b$ and the line $\_a$ construct the angle bisector $\_s_{c}$ (rule W17);
24. Using the line $\_s_{c}$ and the line $\_c$ construct the point $\_T_{c}$ (rule W03);

Statement:
Prove that the point $H_{c}$ is identical to the point $\_H_{c}$.

