






Place the vertices of the right triangle at convenient points: ,
, and
. Then:
is the point
;
is the point
;
is the point
.

Using the given coordinates, we find:
Using the given coordinates, we find:

Using the given coordinates, we find:

Follows from

Follows from
Takeaway
In any right triangle, the following statements are equivalent:
- the right triangle is isosceles
- the Kosnita point coincides with the centroid.
Task
- (Foot of the symmedian) Let
be a triangle having vertices at
,
,
. VERIFY that:
- the foot of the symmedian from
is
- the foot of the symmedian from
is equidistant from the feet of the altitudes from
and
.
- the foot of the symmedian from