Вы имеете в виду биссектрисы? По-английски они называются angle bisectors, в то время как серединные перпендикуляры называются perpendicular bisectors.
If you mean angle bisectors, then
Wikipedia says the radius of the inscribed circle is $r=(a+b-c)/2$ where $a$ and $b$ are legs and $c$ is the hypotenuse. Thus, if we arrange the triangle so that its right angle is in the origin and legs go along the $x$ and $y$ axes, respectively, then the coordinates if the inscribed circle center (which is also the intersection point of angle bisectors) will be $(r,r)$. The hypotenuse ends will have coordinates $(12,0)$ and $(0,9)$, so it is possible to find the middle $D$ of that segment. The intersection point of medians lies $2/3$ of the way from $(0,0)$ to $D$. This way you can find the coordinates of the intersection of medians. Then find the distance according to the usual formula for two points with known coordinates.
