In the triangle
let
and
be the midpoints of the sides
and
respectively and
the foot of the altitude passing through the vertex
. Prove that the circumcircles of the triangles
,
, and
have a common point
and that the line
passes through the midpoint of the segment
%V0
In the triangle $ABC$ let $B'$ and $C'$ be the midpoints of the sides $AC$ and $AB$ respectively and $H$ the foot of the altitude passing through the vertex $A$. Prove that the circumcircles of the triangles $AB'C'$,$BC'H$, and $B'CH$ have a common point $I$ and that the line $HI$ passes through the midpoint of the segment $B'C'.$
Školjka