Question

Hello) i need some help with b) include an explanation if not a problem, thanks in advance)

Answer 1

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