Assuming the vertex is at c, The Pythagorean theorem tells you
.. ab = √(ac^2 +bc^2)
Because all the triangles are similar,
.. cd/bc = ac/ab
.. cd = ac*bc/√(ac^2 +bc^2)
Likewise,
.. ad/ac = ac/ab
.. ad = ac^2/√(ac^2 +bc^2)
Your segments are
.. ad = ac^2/√(ac^2 +bc^2)
.. ab = √(ac^2 +bc^2)
.. dc = ac*bc/√(ac^2 +bc^2)
