Showing that X lies on a line
Proof by contradiction
What would happen if X doesn't lie on OM? If it is true that X lies on OM, if we suppose the opposite then we should have a contradiction, so the only way the contradiction doesn't happen is that it is true
Statements
1. We know that BX:XA = 1:2
2. We know that M is the middle point between B and P
We need to prove that X lies on OM
Let's suppose X doesn't lie on OM
By 2, we know that 2BM = BP
If X doesn't lie on OM then the intersection between OM and BA is not X
Let's say the line that goes from O to the line BP and intersects BA on X is OX', where X'≠M