7.6 esercizio
Given A and C show that exist a point H such that A*H*C
Step 1
Take A,B,C such in figure and the line f and g.
Step 2
Take D and E such that A*B*D and A*C*E. Take h line through D,C and i line trough B,E. They meet in the point F for B4, because taken the triangle ABE the line h cut the side AE in the point C, so it has to cut another side and it cannot be AB because f and h already meet in D. So it exist F on BE segment.
Step 3
Take G such that G*A*B and the line k trough F and G.
k meet BC because if we look at the triangle DBC it cuts DC in F so it has to cut BC, (it cannot cut BD because k and f meet in G). At this point look at the triangle ABC, k cut BC so it has to cut another side, but it can only cut AC because AB in on f and f and k meet in G. So we found the point H such that A*H*C given A and C.