.
is internally tangent to 
and also tangent to 
at 
.
and 
intersect 
and 
respectively. Let 
and 
be points on line 
is the midpoint of 
and 
is the midpoint of 
.
and 
meet at 
and intersect 
and 
respectively. The ray 
meets the circumcircle of triangle 
again at 
.
.
its circumcentre. A line tangent to the circumcircle of the triangle 
intersects sides 
.
be the image of 
.
is tangent to the circumcircle of triangle 
be a semicircle with diameter 
touches 
in a point 
touches 
and 
and 
are perpendicular.
with no parallel sides is inscribed in a circle 
.
are inscribed in triangles 
,
and 
,
,
,
.
Y by Adventure10
Let 
an acute triangle.
(a) Find the locus of points that are centers of rectangles whose vertices lie on the sides of;
(b) Determine if exist some points that are centers of
distinct rectangles whose vertices lie on the sides of .
an acute triangle.(a) Find the locus of points that are centers of rectangles whose vertices lie on the sides of
;(b) Determine if exist some points that are centers of
distinct rectangles whose vertices lie on the sides of .
and 
is the midpoint of 
is the midpoint of 
.
.
.
the midpoints of the side segments 
the midpoints of the altitudes of 
through vertices 
is the concurrency point of the segment lines 
not necessary coincided with the incenter of 
