and 
.
be a triangle with its 9-point center 
and excentral triangle 
.
-
,
,
as 
,
and 
for the 
-
-
,
,
.
be the radical center of the circles 
,
,
.
,
,
are concurrent.
,
and incentral triangle 
.
intersect 
again at 
.
and 
.
and 
be the 9-point centers of 
,
,
are collinear.
be an isogonal conjugate pair. Suppose the line through 
and perpendicular to 
intersects 
again at 
.
.
and perpendicular to 
intersects 
again at 
.
.
and 
be the orthocenters of 
and 
,
and 
.
and 
be the isogonal conjugates of 
with respect to 
are concurrent.
Y by
From a sheet of iron, Petya cut out a square with a side of 
cm and four isosceles triangles with a base cm and a lateral side 
cm. These parts glued , created a regular quadrangular pyramid without gaps in the joints. It is known that with the most economical grinding, metal will go to waste. Find the thickness of the iron sheet.
cm and four isosceles triangles with a base cm and a lateral side 
cm. These parts glued , created a regular quadrangular pyramid without gaps in the joints. It is known that with the most economical grinding, metal will go to waste. Find the thickness of the iron sheet.This post has been edited 2 times. Last edited by parmenides51, Jan 10, 2021, 8:00 AM
