Right-angled triangle with known inradius and altitude-2

Let r is the radius of incircle and h = a is the altitude=side of the right-angled triangle.
Construct this triangle.

Construction:

1. Draw the right angle AOB
2. On side AO, find the points C, and D such that:
   OC = r and OD = a
3. On side BO, find the points F, E, such that:
   OF = a - 2r and FE = r
4. Draw the segment FD
5. From the point E, draw the line parallel to FD, 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. Draw the arc with center at point C and with the radius equal to OD = a
9. Find point H of intersection of arc in p. 8 with semicircle in p. 7

The triangle CHG is the triangle in question.

The case when altitude is to hyponenuse see here.