# Inner/Outer Triangles

- Author:
- Terry Tam

- Topic:
- Triangles

For triangle ABC and an arbitrary point P,
- Triangle DEF is the

**medial**triangle (all vertices are midpoints of the original triangle sides) - Triangle GHI is the**orthic**triangle (all vertices are feet of attitudes of original triangle vertices to the opposite sidelines) - Triangle RST is the**cevian**triangle of point P (all vertices are the intersection points of the lines joining point P and the original triangle vertices to the opposite sidelines) - Triangle P_{A}P_{B}P_{C}is the**pedal**triangle of point P (all vertices are the feet of attitudes of point P to the original triangle sidelines) Try to drag point P (even outside the triangle ABC) or triangle vertices (even crossing the opposite side) to see the changes of four triangles.