SOLUTION: Construct a right triangle such that the bisector of the right angle divides the hypotenuse into segments whose lengths are r and s. I need help on how to tackle this construct

Click here to see ALL problems on Geometry proofs

Question 1182173: Construct a right triangle such that the bisector of the right angle divides
the hypotenuse into segments whose lengths are r and s.
I need help on how to tackle this construction. Even just a hint. Btw, I started constructing perpendicular lines and its bisector but I'm just lost on what to do next to divide the hypotenuse into r and s.
Answer by MathLover1(20850) (Show Source):
You can put this solution on YOUR website!

Use the orthodox method to construct a right triangle.
Then construct the bisector of the right angle (let say vertices C), draw an arc with center at R (on one leg) and another arc with center at V (on the other leg of triangle) with same radius intersecting each other. Join the intersection point and P. Draw a line segment from C through P all way to the hypothenuse. Mark that intersection point with N. So, the line segment CN is the bisector of the right angle and divides hypothenuse into segments whose lengths are r and s.
Note r and s are same length because the bisector of the right angle divides angle into two 45 degree angles, and N is actually midpoint of the hypothenuse

or, you can do it this way:
Place a tip of compass on one of the vertex of triangle.
For one side, open the compass more than the half and draw the curve.
Similarly, do this for same side on opposite vertex.
Where the curves meet at two points, join them.
Similarly, do this for other sides.
You will find that their point of intersection will be mid-point of hypotenuse.