Problem 125:
Given a point $B$, a point $O$ and a point $H_{c}$, construct the triangle ABC.

Construction: 
1. Using the point $B$ and the point $H_{c}$, construct a line $c$ (rule W02);
2. Using the point $B$ and the point $O$, construct a circle $k(O,C)$ (rule W06);
3. Using the circle $k(O,C)$, the line $c$, the point $O$ and the point $B$, construct a point $A$ (rule W05);
4. Using the point $H_{c}$ and the line $c$, construct a line $h_{c}$ (rule W10b);
5. Using the circle $k(O,C)$ and the line $h_{c}$, construct a point $C$ and a point $C_{k}$ (rule W04);
6. Using the point $A$ and the point $C$ construct the line $\_b$ (rule W02);
7. Using the point $C$ and the point $A$, construct a point $\_M_{b}$ (rule W01);
8. Using the point $B$ and the point $C$ construct the line $\_a$ (rule W02);
9. Using the point $B$ and the point $C$, construct a point $\_M_{a}$ (rule W01);
10. Using the point $\_M_{a}$ and the line $\_a$ construct the line $\_m_{a}$ (rule W10b);
11. Using the point $\_M_{b}$ and the line $\_b$ construct the line $\_m_{b}$ (rule W10b);
12. Using the line $\_m_{a}$ and the line $\_m_{b}$ construct the point $\_O$ (rule W03);
13. Using the point $A$ and the point $B$ construct the line $\_c$ (rule W02);
14. Using the point $C$ and the line $\_c$ construct the line $\_h_{c}$ (rule W10b);
15. Using the line $\_c$ and the line $\_h_{c}$ construct the point $\_H_{c}$ (rule W03);

Statement:
Prove that the point $O$ is identical to the point $\_O$.

