Problem 151:
Given a point $B$, a point $M_{b}$ and a point $I$, construct the triangle ABC.

Construction: 
1. Using the point $M_{b}$ and the point $I$, construct a line $IM_{b}$ (rule W02);
2. Using the point $I$ and the point $M_{b}$, construct a circle $k_over(I,M_{b})$ (rule W09);
3. Using the point $B$ and the line $IM_{b}$, construct a line $BP`_{b}$ (rule W16);
4. Using the point $M_{b}$, the line $BP`_{b}$ and the point $B$, construct a line $h_{M_{b},-1/1}(BP`_{b})$ (rule W15);
5. Using the circle $k_over(I,M_{b})$ and the line $h_{M_{b},-1/1}(BP`_{b})$, construct a point $B_{fo}$ and a point $P_{b}$ (rule W04);
6. Using the point $P_{b}$ and the point $I$, construct a circle $k(I,P_{a})$ (rule W06);
7. Using the circle $k(I,P_{a})$, the point $B$ and the point $I$, construct a line $c$ and a line $a$ (rule W12);
8. Using the circle $k(I,P_{a})$, the point $M_{b}$ and the point $I$, construct a line $x2$ and a line $b$ (rule W12);
9. Using the line $c$ and the line $b$, construct a point $A$ (rule W03);
10. Using the point $M_{b}$ and the point $A$, construct a point $C$ (rule W01);
11. Using the point $C$ and the point $A$, construct a point $\_M_{b}$ (rule W01);
12. Using the point $A$ and the point $B$ construct the line $\_c$ (rule W02);
13. Using the point $B$ and the point $C$ construct the line $\_a$ (rule W02);
14. Using the point $A$ and the point $C$ construct the line $\_b$ (rule W02);
15. 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);
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 $B$ is identical to the point $B$.

