lies inside triangle 
and 
.
is the midpoint of segment 
.
lies on segment 
with 
.
.
Y by farhad.fritl, cubres, Rounak_iitr, steppewolf
Let 
be an acute triangle. Points 
and 
lie on a line in this order and satisfy 
. Let 
and 
be midpoints of 
and 
, respectively. Suppose triangle 
is acute, and let 
be its orthocentre. Points 
and 
lie on lines 
and 
, respectively, such that 
and are concyclic and pairwise different, and 
and are concyclic and pairwise different. Prove that 
and are concyclic. 
The orthocentre of a triangle is the point of intersection of its altitudes.
be an acute triangle. Points 
and 
lie on a line in this order and satisfy 
. Let 
and 
be midpoints of 
and 
, respectively. Suppose triangle 
is acute, and let 
be its orthocentre. Points 
and 
lie on lines 
and 
, respectively, such that 
and are concyclic and pairwise different, and 
and are concyclic and pairwise different. Prove that 
and are concyclic. 
The orthocentre of a triangle is the point of intersection of its altitudes.
