Question 20
In trapezoid $ABCD$, $AB\parallel CD$ and diagonals $AC,BD$ intersect at $I$. The area of triangle $ICD$ equals half the area of the trapezoid.
(a) Find $AB/CD$.
(b) Let $M$ be the midpoint of $AB$, and let ray $MI$ meet $CD$ at $N$. Choose $J$ on $IN$. The lines through $J$ parallel to $AC$ and $BD$ meet $AD$ and $BC$ at $E$ and $F$, respectively. If $E,I,F$ are collinear, prove $IM=JN$.
(a) Find $AB/CD$.
(b) Let $M$ be the midpoint of $AB$, and let ray $MI$ meet $CD$ at $N$. Choose $J$ on $IN$. The lines through $J$ parallel to $AC$ and $BD$ meet $AD$ and $BC$ at $E$ and $F$, respectively. If $E,I,F$ are collinear, prove $IM=JN$.