Problem 240:
Given a point $C$, a point $G$ and a point $H_{b}$, construct the triangle ABC.

Construction: 
1. Using the point $C$ and the point $G$, construct a point $M_{c}$ (rule W01);
2. Using the point $C$ and the point $H_{b}$, construct a line $b$ (rule W02);
3. Using the point $H_{b}$ and the point $M_{c}$, construct a circle $k(M_{c},A)$ (rule W06);
4. Using the circle $k(M_{c},A)$, the line $b$, the point $M_{c}$ and the point $H_{b}$, construct a point $A$ (rule W05);
5. Using the point $G$ and the point $A$, construct a point $M_{a}$ (rule W01);
6. Using the point $C$ and the point $M_{a}$, construct a point $B$ (rule W01);
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 a point $\_M_{a}$ (rule W01);
9. Using the point $A$ and the point $\_M_{a}$ construct the line $\_t_{a}$ (rule W02);
10. Using the point $B$ and the point $\_M_{b}$ construct the line $\_t_{b}$ (rule W02);
11. Using the line $\_t_{a}$ and the line $\_t_{b}$ construct the point $\_G$ (rule W03);
12. Using the point $A$ and the point $C$ construct the line $\_b$ (rule W02);
13. Using the point $B$ and the line $\_b$ construct the line $\_h_{b}$ (rule W10b);
14. Using the line $\_b$ and the line $\_h_{b}$ construct the point $\_H_{b}$ (rule W03);

Statement:
Prove that the point $C$ is identical to the point $C$.

