Hosam's Inspheres

Given a tetrahedron $ABCD$ with $A(0, 0, 0), B(10, 0, 0), C(0, 10, 0) , D(1, 1, 10)$ , you select a point $P(x, y, z)$ inside it and you connect $PA , PB , PC , PD$ , thus segmenting tetrahedron $ABCD$ into tetrahedrons $PABC , PABD, PACD, PBCD$ . Find the location of point $P$ such that the inspheres of these four small tetrahedrons have the same radius $r$ . As your answer, enter $\lfloor 10^5 (x + y + z + r ) \rfloor$ .