Problem 176:
Given a point $B$, a point $H_{b}$ and a point $H_{c}$, construct the triangle ABC.

Construction: 
1. Using the point $B$ and the point $H_{b}$, construct a line $h_{b}$ (rule W02);
2. Using the point $B$ and the point $H_{c}$, construct a line $c$ (rule W02);
3. Using the point $H_{b}$ and the line $h_{b}$, construct a line $b$ (rule W10a);
4. Using the line $b$ and the line $c$, construct a point $A$ (rule W03);
5. Using the point $H_{c}$ and the line $c$, construct a line $h_{c}$ (rule W10b);
6. Using the line $b$ and the line $h_{c}$, construct a point $C$ (rule W03);
7. Using the point $A$ and the point $C$ construct the line $\_b$ (rule W02);
8. Using the point $B$ and the line $\_b$ construct the line $\_h_{b}$ (rule W10b);
9. Using the line $\_b$ and the line $\_h_{b}$ construct the point $\_H_{b}$ (rule W03);
10. Using the point $A$ and the point $B$ construct the line $\_c$ (rule W02);
11. Using the point $C$ and the line $\_c$ construct the line $\_h_{c}$ (rule W10b);
12. Using the line $\_c$ and the line $\_h_{c}$ construct the point $\_H_{c}$ (rule W03);

Statement:
Prove that the point $H_{c}$ is identical to the point $\_H_{c}$.

