Angle bisectors of a quadrilateral

[dalcde]

What are the conditions to have such that the angle bisectors of a quadrilateral meet at a single point?

Btw, should I put this in the (Topology and) Geometry forums, or is it for more advanced geometry?

 

[tiny-tim]

hi dalcde!

hmm … angle bisectors …

hint: perpendiculars? ​

 

[dalcde]

The perpendiculars are equal?

Actually that's what I was starting with. You can put a circle around a quadrilateral (enclosing the quadrilateral inside) if and only if opposite angles of the quadrilateral are supplementary. I wanted to know under what conditions will it be possible to put a circle inside that is tangent to all of the side. (analogous to the incenter of a triangle) If having equal perpendiculars is what you meant, I would be going in circles, unless you have some ways to determine if you can put a circle inside, which would be really appreciated.

 

[dalcde]

Anyway, I've found the answer - Pitot Theorem. Thanks anyway.