,
be the projection from 
onto 
.
be a point on the extension of 
.
be on the perpendicular bisector of 
such that 
are on the same side of ![\[\frac12\angle ALE=1.4\angle ABE+3.4\angle ACE-558^\circ\]](http://latex.artofproblemsolving.com/c/6/3/c63eeb053f1fa8a29bef93516814ae121382219e.png)
Let the reflection of 
be 
and 
,
and 
such that 
.
and 
intersect the circumcircles of 
and 
at 
and 
,
and 
intersect 
and 
at 
and 
.
intersect 
.
sastifying 
Y by
Consider a triangle 
. The midpoints of the sides 
, and 
are denoted by 
, and 
, respectively. Assume that the median 
is perpendicular to the median 
and that their lengths are given by 
and 
. Compute the length of the third median 
.
(K. Czakler, Vienna)
. The midpoints of the sides 
, and 
are denoted by 
, and 
, respectively. Assume that the median 
is perpendicular to the median 
and that their lengths are given by 
and 
. Compute the length of the third median 
.(K. Czakler, Vienna)
This post has been edited 3 times. Last edited by parmenides51, May 9, 2024, 5:37 PM
