Problem 4

Construct a right triangle with a given hypotenuse

c

such that the median drawn to the hypotenuse is the geometric mean of the two legs.

Step 3 of 4: Construct the third vertex

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\text{Draw a circle with diameter }AB=c\text{ and a parallel line at distance }c/4

Detailed analysis

Draw $AB=c$ and the circle with diameter $AB$ . Draw either line parallel to $AB$ at distance $c/4$ . Its intersection points with the circle are possible third vertices $C$ , because $\angle ACB=90^\circ$ and the altitude to $AB$ is $c/4$ .