Problem 89:
Given a point $A$, a point $H_{b}$ and a point $T_{c}$, construct the triangle ABC.

Construction: 
1. Using the point $A$ and the point $H_{b}$, construct a line $b$ (rule W02);
2. Using the point $A$ and the point $T_{c}$, construct a line $c$ (rule W02);
3. Using the point $H_{b}$ and the line $b$, construct a line $h_{b}$ (rule W10b);
4. Using the line $h_{b}$ and the line $c$, construct a point $B$ (rule W03);
5. Using the point $A$, the point $B$, the point $T_{c}$ and the line $c$, construct a point $T`_{c}$ (rule W19);
6. Using the point $T_{c}$ and the point $T`_{c}$, construct a circle $k_over(T_{c},T`_{c})$ (rule W09);
7. Using the circle $k_over(T_{c},T`_{c})$ and the line $b$, construct a point $C_{wa}$ and a point $C$ (rule W04);
8. Using the point $A$ and the point $C$ construct the line $\_b$ (rule W02);
9. Using the point $B$ and the line $\_b$ construct the line $\_h_{b}$ (rule W10b);
10. Using the line $\_b$ and the line $\_h_{b}$ construct the point $\_H_{b}$ (rule W03);
11. Using the point $B$ and the point $C$ construct the line $\_a$ (rule W02);
12. Using the point $A$, the point $C$ and the point $B$ and the line $\_b$ and the line $\_a$ construct the angle bisector $\_s_{c}$ (rule W17);
13. Using the point $A$ and the point $B$ construct the line $\_c$ (rule W02);
14. Using the line $\_s_{c}$ and the line $\_c$ construct the point $\_T_{c}$ (rule W03);

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

