is integer, find the possible values of 
.
,
,
.
be the orthocenter of 
.
a
.
and 
are parallelograms.
, such that 
Prove that :
equality cases : ?
be the incenter, centroid and the circumcenter of triangle 
be on the rays 
respectively so that 
.
be the centroid of 
.
is perpendicular to 
.
Y by
In an arbitrary triangle 
, point 
is the midpoint of the side 
, point 
is the foot of the angle bisector from vertex 
, point 
is the intersection point of the bisector 
with the circumscribed circle, points 
and 
are the centers of exscribed circles tangent to sides 
and 
, respectively. Prove that
a) points
lie on one circle;
b) is the orthocenter of the triangle 
.
(D. Basov, Y. Biletsky)
, point 
is the midpoint of the side 
, point 
is the foot of the angle bisector from vertex 
, point 
is the intersection point of the bisector 
with the circumscribed circle, points 
and 
are the centers of exscribed circles tangent to sides 
and 
, respectively. Prove thata) points
lie on one circle;b)
is the orthocenter of the triangle 
.(D. Basov, Y. Biletsky)
This post has been edited 1 time. Last edited by parmenides51, Jul 4, 2021, 11:54 PM
