Median between sides

A triangle has sides a,b,c and the medians d,e,f ending at those sides, respectively. Given the lengths (a,b,f) construct the triangle. (Start with a triangle with side lengths determined in some manor from the given 3 lengths.)

Scroll down for a solution to this problem.


Solution by Stéphane Bernard.

I would start with 2f at the base and add the sides a,b then slide a along b and b along a to make a parallelogram (or rotate the triangle around center of 2f) Then join the vertices at (a,b) to make the side c. Apollonius would be proud!

🤞 Don’t miss these puzzles!

Subscribe to the weekly geometry puzzle e-mail.

Leave a Reply

Your email address will not be published. Required fields are marked *

Optionally add an image (JPEG only)