Problem 186:
Given a point $B$, a point $H_{c}$ and a point $I$, construct the triangle ABC.

Construction: 
1. Using the point $B$ and the point $H_{c}$, construct a line $c$ (rule W02);
2. Using the point $H_{c}$ and the line $c$, construct a line $h_{c}$ (rule W10b);
3. Using the point $I$ and the line $c$, construct a circle $k(I,P_{a})$ (rule W11);
4. Using the circle $k(I,P_{a})$, the point $B$, the point $I$ and the line $c$, construct a line $a$ (rule W13);
5. Using the line $a$ and the line $h_{c}$, construct a point $C$ (rule W03);
6. Using the circle $k(I,P_{a})$, the point $C$, the point $I$ and the line $a$, construct a line $b$ (rule W13);
7. Using the line $b$ and the line $c$, construct a point $A$ (rule W03);
8. Using the point $A$ and the point $B$ construct the line $\_c$ (rule W02);
9. Using the point $C$ and the line $\_c$ construct the line $\_h_{c}$ (rule W10b);
10. Using the line $\_c$ and the line $\_h_{c}$ construct the point $\_H_{c}$ (rule W03);
11. Using the point $B$ and the point $C$ construct the line $\_a$ (rule W02);
12. Using the point $A$ and the point $C$ construct the line $\_b$ (rule W02);
13. 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);
14. 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);
15. Using the line $\_s_{a}$ and the line $\_s_{b}$ construct the point $\_I$ (rule W03);

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

