Hello, Shnub!

Given right triangle $\displaystyle ABC$ with $\displaystyle D$ the midpoint of hypotenuse $\displaystyle AB$,

show that $\displaystyle D$ is equidistant from $\displaystyle B$ and $\displaystyle C.$ Code:

* * *
* * C
* o
* * *
*
* * *
A o - - - - o - - - - o B
* D *
* *
* *
* *
* * *

Draw $\displaystyle AC$ and $\displaystyle BC.$

A right triangle can be inscribed in a semicircle.

The midpoint of the hypotenuse is the center of the circle.

Therefore: .$\displaystyle DA = DB = DC = \text{radius}$