Problem 429:
Given a point $M_{b}$, 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 point $M_{b}$, construct a circle $k(M_{b},C)$ (rule W06);
3. Using the circle $k(M_{b},C)$, the line $c$, the point $M_{b}$ and the point $H_{c}$, construct a point $A$ (rule W05);
4. Using the point $A$ and the point $M_{b}$, construct a point $C$ (rule W01);
5. Using the point $M_{b}$ and the point $A$, construct a line $b$ (rule W02);
6. Using the point $T_{c}$ and the line $b$, construct a circle $k(T_{c},foot[T_{c},b])$ (rule W11);
7. Using the circle $k(T_{c},foot[T_{c},b])$, the point $C$, the point $T_{c}$ and the line $b$, construct a line $a$ (rule W13);
8. Using the line $a$ and the line $c$, construct a point $B$ (rule W03);
9. Using the point $C$ and the point $A$, construct a point $\_M_{b}$ (rule W01);
10. Using the point $A$ and the point $B$ construct the line $\_c$ (rule W02);
11. Using the point $C$ and the line $\_c$ construct the line $\_h_{c}$ (rule W10b);
12. Using the line $\_c$ and the line $\_h_{c}$ construct the point $\_H_{c}$ (rule W03);
13. Using the point $B$ and the point $C$ construct the line $\_a$ (rule W02);
14. Using the point $A$ and the point $C$ construct the line $\_b$ (rule W02);
15. 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);
16. Using the line $\_s_{c}$ and the line $\_c$ construct the point $\_T_{c}$ (rule W03);

Statement:
Prove that the point $M_{b}$ is identical to the point $\_M_{b}$.

