Problem 522:
Given a point $H_{a}$, a point $T_{a}$ and a point $I$, construct the triangle ABC.

Construction: 
1. Using the point $H_{a}$ and the point $T_{a}$, construct a line $a$ (rule W02);
2. Using the point $T_{a}$ and the point $I$, construct a line $s_{a}$ (rule W02);
3. Using the point $H_{a}$ and the line $a$, construct a line $h_{a}$ (rule W10b);
4. Using the line $h_{a}$ and the line $s_{a}$, construct a point $A$ (rule W03);
5. Using the point $I$ and the line $a$, construct a circle $k(I,P_{a})$ (rule W11);
6. Using the circle $k(I,P_{a})$, the point $A$ and the point $I$, construct a line $c$ and a line $b$ (rule W12);
7. Using the line $c$ and the line $a$, construct a point $B$ (rule W03);
8. Using the line $a$ and the line $b$, construct a point $C$ (rule W03);
9. Using the point $B$ and the point $C$ construct the line $\_a$ (rule W02);
10. Using the point $A$ and the line $\_a$ construct the line $\_h_{a}$ (rule W10b);
11. Using the line $\_a$ and the line $\_h_{a}$ construct the point $\_H_{a}$ (rule W03);
12. Using the point $A$ and the point $C$ construct the line $\_b$ (rule W02);
13. Using the point $A$ and the point $B$ construct the line $\_c$ (rule W02);
14. Using the point $B$, the point $A$ and the point $C$ and the line $\_c$ and the line $\_b$ construct the angle bisector $\_s_{a}$ (rule W17);
15. Using the line $\_s_{a}$ and the line $\_a$ construct the point $\_T_{a}$ (rule W03);
16. Using the point $C$, the point $B$ and the point $A$ and the line $\_a$ and the line $\_c$ construct the angle bisector $\_s_{b}$ (rule W17);
17. Using the line $\_s_{a}$ and the line $\_s_{b}$ construct the point $\_I$ (rule W03);

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

