$(a)$ Let $\triangle{ABC}$ have incenter $I$ and incircle tangent $BC,CA,AB$ at $D,E,F$ respectively Then draw three segment $ID,IE,IF$ and we are done. $(b)$ Let $X$ is foot of altitude from $A$ and $Y,Z$ are midpoints of $AB,AC$ Then draw two segment $YX,ZX$ give us $\triangle{YBX},\triangle{ZXC}$ are isoscele triangles and quadrilateral $AYXZ$ have symmetry axis $YZ$, so we are done.