Question 10
Consider a triangle $ABC$, such that $\angle B = 90^\circ$. Denote by $I$ the in-center and let $F$, $D$ and $E$ be the points where the incircle touches sides $[AB]$, $[BC]$, and $[AC]$ respectively. If $CI \cap EF = \{M\}$ and $DM \cap AB = \{N\}$, show that:
a) $AI = ND$;
b) $FM = \frac{EI \cdot EM}{EC}$.
a) $AI = ND$;
b) $FM = \frac{EI \cdot EM}{EC}$.