be an acute triangle with 
,
be the projection from 
onto 
.
be a point on the extension of 
past 
.
be on the perpendicular bisector of 
such that ![\[\frac12\angle ALE=1.4\angle ABE+3.4\angle ACE-558^\circ\]](http://latex.artofproblemsolving.com/c/6/3/c63eeb053f1fa8a29bef93516814ae121382219e.png)
Let the reflection of 
and 
,
and 
such that 
.
and 
intersect the circumcircles of 
and 
at 
and 
,
and 
intersect 
and 
at 
and 
.
intersect 
.
.
and 
.
.
be the point on 
Y by
In a circle with center 
, chords 
and 
are drawn, both equal to the radius. Points 
, 
and 
are projections of points 
and 
, respectively, onto an arbitrary diameter 
. Prove that one of the segments 
, 
and 
is equal to the sum of the other two.
(A. Shklover)
, chords 
and 
are drawn, both equal to the radius. Points 
, 
and 
are projections of points 
and 
, respectively, onto an arbitrary diameter 
. Prove that one of the segments 
, 
and 
is equal to the sum of the other two.(A. Shklover)
This post has been edited 1 time. Last edited by parmenides51, Apr 18, 2022, 7:33 AM
and 
and 
and 
.
one of 
is sum of the other two.
and 
and 
.
such that 
.
or 
or 
.
and 
so 
and 
are congruent so 
is a rhombus, the projections of 
onto 
.
.
