Geometry Problem 1486: Right Triangle, Altitude, Incircle, Tangent, Measurement

The figure shows a right triangle ABC with altitude BD and AC tangent to the incircle at E. If the measure of inradii of triangles ADB and BDC are 3 and 4, respectively, find the measure of DE.
Geometry Problem 1486: Right Triangle, Altitude, Incircle, Tangent, Measurement

Incircle

Incircle is a circle within a triangle, that is tangent to each side.