Problem 479:
Given a point $G$, a point $H_{a}$ and a point $H$, construct the triangle ABC.

Construction: 
1. Using the point $G$ and the point $H$, construct a point $O$ (rule W01);
2. Using the point $H_{a}$ and the point $H$, construct a line $h_{a}$ (rule W02);
3. Using the point $H_{a}$ and the line $h_{a}$, construct a line $a$ (rule W10a);
4. Using the point $O$ and the line $a$, construct a line $m_{a}$ (rule W10b);
5. Using the line $m_{a}$ and the line $a$, construct a point $M_{a}$ (rule W03);
6. Using the point $M_{a}$ and the point $G$, construct a point $A$ (rule W01);
7. Using the point $A$ and the point $O$, construct a circle $k(O,C)$ (rule W06);
8. Using the circle $k(O,C)$ and the line $a$, construct a point $C$ and a point $B$ (rule W04);
9. Using the point $C$ and the point $A$, construct a point $\_M_{b}$ (rule W01);
10. Using the point $B$ and the point $C$, construct a point $\_M_{a}$ (rule W01);
11. Using the point $A$ and the point $\_M_{a}$ construct the line $\_t_{a}$ (rule W02);
12. Using the point $B$ and the point $\_M_{b}$ construct the line $\_t_{b}$ (rule W02);
13. Using the line $\_t_{a}$ and the line $\_t_{b}$ construct the point $\_G$ (rule W03);
14. Using the point $B$ and the point $C$ construct the line $\_a$ (rule W02);
15. Using the point $A$ and the line $\_a$ construct the line $\_h_{a}$ (rule W10b);
16. Using the line $\_a$ and the line $\_h_{a}$ construct the point $\_H_{a}$ (rule W03);
17. Using the point $A$ and the point $C$ construct the line $\_b$ (rule W02);
18. Using the point $B$ and the line $\_b$ construct the line $\_h_{b}$ (rule W10b);
19. Using the line $\_h_{a}$ and the line $\_h_{b}$ construct the point $\_H$ (rule W03);

Statement:
Prove that the point $H$ is identical to the point $\_H$.

