7. In square $\mathrm{ABCD}, \overline{A C}$ and $\overline{B D}$ meet at point $\mathrm{E}$.
Point $\mathrm{F}$ is on $\overline{C D}$ and $\angle C A F=\angle F A D$.
If $\overline{A F}$ meets $\overline{E D}$ at point $\mathrm{G}$, and if $\overline{E G}=24 \mathrm{~cm}$, then find the length of $\overline{C F}$.
7. Draw $\mathrm{EK} \| \mathrm{DC}$ with $\mathrm{K}$ on $\mathrm{AF}$. In right triangle $\mathrm{AEG}, \angle \mathrm{AGE}=67.5$; and $\angle \mathrm{EKG}=$ $<\mathrm{KAE}+<\mathrm{AEK}=67.5$.
Hence triangle $\mathrm{KEG}$ is isosceles and $\mathrm{FC}=2 \mathrm{KE}=2 \mathrm{EG}=48$