Problem 218:
Given a point $C$, a point $M_{a}$ and a point $T_{c}$, construct the triangle ABC.

Construction: 
1. Using the point $C$ and the point $M_{a}$, construct a point $B$ (rule W01);
2. Using the point $C$ and the point $M_{a}$, construct a line $a$ (rule W02);
3. Using the point $T_{c}$ and the point $B$, construct a line $c$ (rule W02);
4. Using the point $T_{c}$ and the line $a$, construct a circle $k(T_{c},foot[T_{c},b])$ (rule W11);
5. Using the circle $k(T_{c},foot[T_{c},b])$, the point $C$, the point $T_{c}$ and the line $a$, construct a line $b$ (rule W13);
6. Using the line $b$ and the line $c$, construct a point $A$ (rule W03);
7. Using the point $B$ and the point $C$, construct a point $\_M_{a}$ (rule W01);
8. Using the point $B$ and the point $C$ construct the line $\_a$ (rule W02);
9. Using the point $A$ and the point $C$ construct the line $\_b$ (rule W02);
10. 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);
11. Using the point $A$ and the point $B$ construct the line $\_c$ (rule W02);
12. Using the line $\_s_{c}$ and the line $\_c$ construct the point $\_T_{c}$ (rule W03);

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

