Problem 425:
Given a point $M_{b}$, a point $H_{b}$ and a point $I$, construct the triangle ABC.

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

