Problem 103:
Given a point $A$, a point $T_{b}$ and a point $T_{c}$, construct the triangle ABC.

Construction: 
1. Using the point $A$ and the point $T_{b}$, 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 line $b$, the point $T_{c}$, the point $A$, the point $T_{b}$ and the line $c$, construct a line $s_{a}$ (rule W17);
4. Using the point $T_{c}$, the point $A$ and the point $T_{b}$, construct a circle $circle[T_{b},T_{c},angle[s[b]][s[c]]]$ (rule W20);
5. Using the circle $circle[T_{b},T_{c},angle[s[b]][s[c]]]$ and the line $s_{a}$, construct a point $A_{sa}$ and a point $I$ (rule W04);
6. Using the point $I$ and the point $T_{b}$, construct a line $s_{b}$ (rule W02);
7. Using the point $T_{c}$ and the point $I$, construct a line $s_{c}$ (rule W02);
8. Using the line $b$ and the line $s_{c}$, construct a point $C$ (rule W03);
9. Using the line $c$ and the line $s_{b}$, construct a point $B$ (rule W03);
10. Using the point $A$ and the point $B$ construct the line $\_c$ (rule W02);
11. Using the point $B$ and the point $C$ construct the line $\_a$ (rule W02);
12. 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);
13. Using the point $A$ and the point $C$ construct the line $\_b$ (rule W02);
14. Using the line $\_s_{b}$ and the line $\_b$ construct the point $\_T_{b}$ (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);

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

