Right-angled triangle with known inradius and altitude

Let r is the radius of incircle and h is the altitude to hypotenuse of the right-angled triangle.
Construct this triangle.

Construction:

1. Draw the right angle AOB
2. On side AO, find the point C, such that OC = 2r
3. On side BO, find the points D, E, H, such that:
   • OE = 2h - 4r
   • OH = h
   • ED = OC = 2r
4. Draw the segment EC
5. From the point D, draw the line parallel to EC, and find point G of intersection with side AO
6. The segment CG is the hypotenuse of the triangle in question
7. Draw the semicircle on CG as diameter
8. From point H draw line parallel to side AO
9. Find point L of intersection of line in p. 8 with semicircle in p. 7

The triangle CLG is the triangle in question.

The case when altitude = side of triangle see here.