Construction of a sphere inscribed in a tetrahedron in GeoGebra

Question

I wonder how can I constuct a sphere inscribed in a tetrahedron using GeoGebra?
I've thought I can construct it using the intersection of three planes bisecting angles between some pairs of faces in a tetrahedron, but when I contructed it, it didn't seem to work.
Is this construction valid and I made some mistake while constructing the planes, or is it not a proper construction? If it is the latter, what is the proper way?

Answer 1

Hint:

1- select 3D

2- select extrude, then tetrahedron.

3- select points A and B, you see the tetrahedron constructed.

4- Consider the fact that the center of the inscribed sphere is where the altitudes of tetrahedron meet. The altitudes are lines perpendicular on each surface from it's opposite vertex, take vertex D and use the command perpendicular from D on face ABC , for this select point D, then plane XY, where face ABC is on.

5- Go to command for construction of plane through three points then select points D,C and B, you will see a plane constructed.

6- similar to 4 drop a perpendicular from A to constructed plane in 5.

7- Go to command for point and select intersection.

8- find the feet of altitudes from D and A by selecting D and XY plane, it gives point E. Similarly find G on face BCD by selecting point A , then plane passing BCD.

9- make intersection of altitudes AG and BE which is point F and is the center of the sphere.

10- finally go to command for construction of the sphere, select F as center then G or E, you will see the sphere constructed.