Track / Stage 5 / 80 of 400 #680 of 2000

## Task 5 - 040815

The following statement is to be proven:

If in a triangle a median is half as long as the corresponding side, then the triangle is a right triangle.

This one wants a proof. Work it on paper, read the official solution, then mark yourself honestly — the ladder only means something if the record is true.

I solved it I didn't Skip

Official solution

According to the conditions of the sentence, the vertices of the triangle lie on the Thales circle over $\overline{A B}$, if $a_{c}$ is the median.

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.