construction of line segment of a length $\sqrt{a^2-b^2+c^2+d^2}$

Question

There are line segments $a, b, c, d$ and $a > b$. I have a question how to construct a line segment of a length $\sqrt{a^2-b^2+c^2+d^2}$. I can use Pythagoras theorem but I don't know how to make use of it. Thanks for any help.

Answer 1

Draw a first right triangle with legs $a$ and $c$, then a second having as a first leg the hypotenuse of the first triangle, and a second leg of length $d$. Finally, draw a third triangle having the same hypotenuse as the second one and a leg equal to $b$. The length of the other leg is your answer.