Problem 559:
Given a point $T_{a}$, a point $T_{c}$ and a point $I$, construct the triangle ABC.

Construction: 
1. Using the point $T_{a}$ and the point $I$, construct a line $s_{a}$ (rule W02);
2. Using the point $T_{c}$ and the point $I$, construct a line $s_{c}$ (rule W02);
3. Using the point $T_{c}$, the point $I$ and the point $T_{a}$, construct a circle $circle[T_{a},I,angle[a][s[b]]]$ (rule W20);
4. Using the point $T_{c}$, the point $I$ and the point $T_{a}$, construct a circle $circle[T_{c},T_{a},angle[a][c]]$ (rule W20);
5. Using the circle $circle[T_{c},T_{a},angle[a][c]]$ and the circle $circle[T_{a},I,angle[a][s[b]]]$, construct a point $B_{c1}$ and a point $B$ (rule W07);
6. Using the point $B$ and the point $T_{a}$, construct a line $a$ (rule W02);
7. Using the point $T_{c}$ and the point $B$, construct a line $c$ (rule W02);
8. Using the line $s_{a}$ and the line $c$, construct a point $A$ (rule W03);
9. Using the line $s_{c}$ and the line $a$, construct a point $C$ (rule W03);
10. Using the point $A$ and the point $C$ construct the line $\_b$ (rule W02);
11. Using the point $A$ and the point $B$ construct the line $\_c$ (rule W02);
12. 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);
13. Using the point $B$ and the point $C$ construct the line $\_a$ (rule W02);
14. Using the line $\_s_{a}$ and the line $\_a$ construct the point $\_T_{a}$ (rule W03);
15. 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);
16. Using the line $\_s_{c}$ and the line $\_c$ construct the point $\_T_{c}$ (rule W03);
17. 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);
18. Using the line $\_s_{a}$ and the line $\_s_{b}$ construct the point $\_I$ (rule W03);

Statement:
Prove that the point $I$ is identical to the point $\_I$.

