Symmedian
Day 2 theme of Mathtober 23 is Symmedian.
Had to remind myself what that means, the reflection of the median across the angle bisectors (isogonal to the medians). And just like the medians are concurrent, then so are the symmedians, and their intersection is the isogonal conjugate to the centroid (the intersection of the medians).
There's an idea called the trilinear coordinates for a point in a triangle, and the trilinear coordinates for the symmedian intersection are the inverse of that for the centroid.
I'm not sure how to produce the trilinear coordinates given a point, nor find a point from the trilinear coordinates. There's always more to learn.
This sketch generalizes the median to the corresponding points parameterized by t, and those segments isogonal segments. Pretty fascinating to me.