Question 38
Let $ABC$ be an acute-angled triangle with $AB \lt AC$. Let
- $D$ be the foot of the bisector of the angle at $A$,
- $E$ be the point of segment $BC$ (different from $B$) such that $AB = AE$,
- $F$ be the point of segment $BC$ (different from $B$) such that $BD = DF$,
- $G$ be the point of segment $AC$ such that $AB = AG$.
Prove that the circumcircle of triangle $EFG$ is tangent to the line $AC$.
- $D$ be the foot of the bisector of the angle at $A$,
- $E$ be the point of segment $BC$ (different from $B$) such that $AB = AE$,
- $F$ be the point of segment $BC$ (different from $B$) such that $BD = DF$,
- $G$ be the point of segment $AC$ such that $AB = AG$.
Prove that the circumcircle of triangle $EFG$ is tangent to the line $AC$.