Question 127
Let $ABC$ be a triangle with $\measuredangle BAC = 60^\circ$. Find all points $P$ inside this triangle with the following property:
If $D$ is the projection of $P$ onto the line $BC$, $E$ is the projection of $P$ onto $CA$ and $F$ is the projection of $P$ onto $AB$, then the following applies $\measuredangle EDF = 30^\circ$.
If $D$ is the projection of $P$ onto the line $BC$, $E$ is the projection of $P$ onto $CA$ and $F$ is the projection of $P$ onto $AB$, then the following applies $\measuredangle EDF = 30^\circ$.