Problem 23:
Given a point $A$, a point $C$ and a point $H$, construct the triangle ABC.

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

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

