Problem 466:
Given a point $M_{c}$, a point $H_{c}$ and a point $I$, construct the triangle ABC.

Construction: 
1. Using the point $M_{c}$ and the point $H_{c}$, construct a line $c$ (rule W02);
2. Using the point $M_{c}$ and the point $I$, construct a line $IM_{c}$ (rule W02);
3. Using the point $I$ and the point $M_{c}$, construct a circle $k_over(I,M_{c})$ (rule W09);
4. Using the point $M_{c}$ and the line $c$, construct a line $m_{c}$ (rule W10b);
5. Using the point $H_{c}$ and the line $c$, construct a line $h_{c}$ (rule W10b);
6. Using the point $I$ and the line $c$, construct a circle $k(I,P_{a})$ (rule W11);
7. Using the circle $k(I,P_{a})$ and the circle $k_over(I,M_{c})$, construct a point $C_{fi}$ and a point $P_{c}$ (rule W07);
8. Using the point $P_{c}$ and the point $M_{c}$, construct a point $P`_{c}$ (rule W01);
9. Using the point $P`_{c}$ and the line $IM_{c}$, construct a line $CP`_{c}$ (rule W16);
10. Using the line $CP`_{c}$ and the line $h_{c}$, construct a point $C$ (rule W03);
11. Using the point $I$ and the point $C$, construct a line $s_{c}$ (rule W02);
12. Using the line $m_{c}$ and the line $s_{c}$, construct a point $N_{c}$ (rule W03);
13. Using the point $I$ and the point $N_{c}$, construct a circle $k(N_{c},B)$ (rule W06);
14. Using the circle $k(N_{c},B)$ and the line $c$, construct a point $B$ and a point $A$ (rule W04);
15. Using the point $A$ and the point $B$, construct a point $\_M_{c}$ (rule W01);
16. Using the point $A$ and the point $B$ construct the line $\_c$ (rule W02);
17. Using the point $C$ and the line $\_c$ construct the line $\_h_{c}$ (rule W10b);
18. Using the line $\_c$ and the line $\_h_{c}$ construct the point $\_H_{c}$ (rule W03);
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 $\_I$.

