NOTE: I want a hint only.
A compass and a straightedge construction:Given a hypotenuse and the sum of lengths of the legs,we need to construct a right triangle.
MY TRY: From any ray $BE$, ,let us cut off $BC$ equal to our hypotenuse.Now we draw a circle with the hypotenuse as diameter.Now,if we take any point on the circle and join it with the end points of the hypotenuse,we will have a right triangle by Thales' theorem.
BACKTRACKING: As is often the case,first assuming that we have constructed our figure and then trying to reverse-engineer the steps helps in construction of the required figure.Suppose we have $\Delta ABC$ inscribed in a circle with $\angle A$ the right angle.We extend one of the legs $BA$ to $K$ such that $BK$ is equal to the sum of the legs of our triangle.Then $AK=AC$ and therefore $\angle AKC=\angle ACK$. Similarly,we extend $AC$ to $L$ such that it is equal to the sum of the legs.Then we can argue about angle equality the same way.But this is not helping me in constructing the right triangle.
A hint will be appreciated.