the third circle

There are three circles which contact each other. How do you draw the third circle?

Three common tangents cross at point P.
The radius of circle O1 is a.The radius of circle O2 is b.The radius of circle O3 is c.The distance between point P and point of contact is t.

What is the relation between a, b, c and t?

Move point A to find the geometric relation betweeen the triangle ABD and the triangle BCD.

@You can move points O1, O2, A, P on CABRI.
Download CABRIU data (d14) from here.