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 .
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 .
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.

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