WOLFRAM|DEMONSTRATIONS PROJECT

Generalized Inscribed and Escribed Triangles

​
inscribed
escribed
α
β
γ
A triangle
ABC
is inscribed in a triangle
PQR
if the vertices of
ABC
lie on different sides of
PQR
. For instance,
A
lying on side
PQ
,
B
lying on side
QR
, and
C
lying on side
RA
. Equivalently,
PQR
is escribed around
ABC
.
Our generalization considers a "side" as meaning the full line passing through two vertices. Then
ABC
can be inscribed into
PQR
and be totally outside of
PQR
, or
PQR
can be escribed around
ABC
and be totally inside
ABC
.
The families of inscribed and escribed triangles depend on three parameters
α
,
β
, and
γ
. 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
ABC
, and triangle
PQR
is generated according to the choice of family.