Problem 267:
Given a point $C$, a point $H$ and a point $T_{c}$, construct the triangle ABC.

Construction: 
1. Using the point $C$ and the point $H$, construct a point $E_{c}$ (rule W01);
2. Using the point $C$ and the point $H$, construct a line $h_{c}$ (rule W02);
3. Using the point $C$ and the point $T_{c}$, construct a line $s_{c}$ (rule W02);
4. Using the point $T_{c}$ and the line $h_{c}$, construct a line $c$ (rule W10a);
5. Using the point $H$, the point $C$, the point $T_{c}$, the line $s_{c}$ and the line $h_{c}$, construct a line $CO$ (rule W17);
6. Using the point $E_{c}$ and the line $CO$, construct a line $m(H_{b}H_{a})$ (rule W16);
7. Using the line $m(H_{b}H_{a})$ and the line $c$, construct a point $M_{c}$ (rule W03);
8. Using the point $M_{c}$ and the point $C$, construct a point $G$ (rule W01);
9. Using the point $H$ and the point $G$, construct a point $O$ (rule W01);
10. Using the point $C$ and the point $O$, construct a circle $k(O,C)$ (rule W06);
11. Using the circle $k(O,C)$ and the line $c$, construct a point $A$ and a point $B$ (rule W04);
12. Using the point $A$ and the point $C$ construct the line $\_b$ (rule W02);
13. Using the point $B$ and the point $C$ construct the line $\_a$ (rule W02);
14. Using the point $A$ and the line $\_a$ construct the line $\_h_{a}$ (rule W10b);
15. Using the point $B$ and the line $\_b$ construct the line $\_h_{b}$ (rule W10b);
16. Using the line $\_h_{a}$ and the line $\_h_{b}$ construct the point $\_H$ (rule W03);
17. 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);
18. Using the point $A$ and the point $B$ construct the line $\_c$ (rule W02);
19. Using the line $\_s_{c}$ and the line $\_c$ construct the point $\_T_{c}$ (rule W03);

Statement:
Prove that the point $T_{c}$ is identical to the point $\_T_{c}$.

