Question 128
In an arbitrary triangle $ABC$, let $M$ and $N$ be the midpoints of the segments $BC$ and $AM$, respectively, let $D$ be the reflection of the point $C$ in $A$, let $BN \cap AC = \{S\}$, $DM \cap AB = \{T\}$, and let $P$ be the midpoint of the segment $[SC]$.
a) Prove that $AC = 3PC$.
b) Prove that the lines $ST$ and $BC$ are parallel.
c) Compute the area of triangle $ANS$, given that the area of triangle $ABC$ equals $48~\mathrm{cm}^2$.
a) Prove that $AC = 3PC$.
b) Prove that the lines $ST$ and $BC$ are parallel.
c) Compute the area of triangle $ANS$, given that the area of triangle $ABC$ equals $48~\mathrm{cm}^2$.