Let 
be a triangle, 
is a any point lie on 
. 
is projections of on 
, 
is projections of on . Cosntruct a conic through 
. 
is orthocenter of the triangle . 
is any point lie on the conic. 
meets 
, at 
. Perpencicular of 
at meets 
respectively at 
.
be a triangle, is a any point lie on . is projections of on , is projections of on . Cosntruct a conic through . is orthocenter of the triangle . is any point lie on the conic. meets , at . Perpencicular of at meets respectively at .
Denote 
respectively are midpoints of 
. Prove that: are collinear
respectively are midpoints of . Prove that: are collinear
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