Problem 529:
Given a point $H_{b}$, a point $H_{c}$ and a point $T_{c}$, construct the triangle ABC.

Construction: 
1. Using the point $H_{b}$ and the point $H_{c}$, construct a line $H_{b}H_{c}$ (rule W02);
2. Using the point $H_{c}$ and the point $T_{c}$, construct a line $c$ (rule W02);
3. Using the point $H_{c}$ and the line $c$, construct a line $h_{c}$ (rule W10b);
4. Using the point $H_{b}$, the point $H_{c}$, the point $T_{c}$, the line $c$ and the line $H_{b}H_{c}$, construct a line $H_{c}H_{a}$ (rule W17);
5. Using the point $H_{b}$, the point $H_{c}$ and the point $T_{c}$, construct a circle $circle[T_{c},H_{b},angle[b][s[c]]]$ (rule W20);
6. Using the circle $circle[T_{c},H_{b},angle[b][s[c]]]$ and the line $h_{c}$, construct a point $C_{ca2}$ and a point $C$ (rule W04);
7. Using the point $C$ and the point $H_{b}$, construct a line $b$ (rule W02);
8. Using the line $c$ and the line $b$, construct a point $A$ (rule W03);
9. Using the point $A$ and the point $C$, construct a point $M_{b}$ (rule W01);
10. Using the point $H_{c}$ and the point $M_{b}$, construct a circle $k(M_{b},C)$ (rule W06);
11. Using the circle $k(M_{b},C)$, the line $H_{c}H_{a}$, the point $M_{b}$ and the point $H_{c}$, construct a point $H_{a}$ (rule W05);
12. Using the point $C$ and the point $H_{a}$, construct a line $a$ (rule W02);
13. Using the line $c$ and the line $a$, construct a point $B$ (rule W03);
14. Using the point $A$ and the point $C$ construct the line $\_b$ (rule W02);
15. Using the point $B$ and the line $\_b$ construct the line $\_h_{b}$ (rule W10b);
16. Using the line $\_b$ and the line $\_h_{b}$ construct the point $\_H_{b}$ (rule W03);
17. Using the point $A$ and the point $B$ construct the line $\_c$ (rule W02);
18. Using the point $C$ and the line $\_c$ construct the line $\_h_{c}$ (rule W10b);
19. Using the line $\_c$ and the line $\_h_{c}$ construct the point $\_H_{c}$ (rule W03);
20. Using the point $B$ and the point $C$ construct the line $\_a$ (rule W02);
21. 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);
22. 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 $\_H_{c}$.

