Question 1
Triangle $ABC$ is isosceles at $A$. Choose $D$ on $BC$ with $BD=BC/3$. Extend ray $AD$ beyond $D$ to $E$ so that $DE=AD$. Extend ray $BE$ beyond $E$ to $F$ so that $BE=EF$.
a) Prove that $FD\perp BC$.
b) If $ABC$ is equilateral with $AB=1$, find $FD$.
a) Prove that $FD\perp BC$.
b) If $ABC$ is equilateral with $AB=1$, find $FD$.