Question 17
Let $ABC$ be a right isosceles triangle with right angle at $A$, $O$ the midpoint of the hypotenuse $BC$, $E$ the midpoint of the segment $CO$, $M$ the midpoint of $AC$, and $D$ the midpoint of $AM$. Let $F$ be the intersection of lines $OD$ and $AE$.
a) Prove that $MF \perp OD$.
b) Prove that $FC = OC$.
a) Prove that $MF \perp OD$.
b) Prove that $FC = OC$.