# Generalized Inscribed and Escribed Triangles

Generalized Inscribed and Escribed Triangles

A triangle is inscribed in a triangle if the vertices of lie on different sides of . For instance, lying on side , lying on side , and lying on side . Equivalently, is escribed around .

ABC

PQR

ABC

PQR

A

PQ

B

QR

C

RA

PQR

ABC

Our generalization considers a "side" as meaning the full line passing through two vertices. Then can be inscribed into and be totally outside of , or can be escribed around and be totally inside .

ABC

PQR

PQR

PQR

ABC

ABC

The families of inscribed and escribed triangles depend on three parameters , , and . This Demonstration lets you explore their roles in the creation of inscribed and escribed triangles by varying them. You can drag the yellow vertices of triangle , and triangle is generated according to the choice of family.

α

β

γ

ABC

PQR