Y by Adventure10, Mango247
. 
.Incircle touches
and 
at 
.Middle line parallel to
cuts 
at 
.Prove that
are lay on circle.Attachments:
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Might be slightly generalizable
Rijul saini 5
N
by guptaamitu1
Source: India IMOTC Day 3 Problem 1
Let 
be an acute angled triangle with orthocenter 
and 
. Let 
be any other point on the arc 
of the circumcircle of 
and let line 
intersect line 
at 
and let line 
intersect line 
at 
. Let the circumcircles of 
and intersect again at 
(
). Let the lines 
intersect the circumcircle of 
again at 
(
). Prove that the lines 
concur.
be an acute angled triangle with orthocenter 
and 
. Let 
be any other point on the arc 
of the circumcircle of 
and let line 
intersect line at 
and let line 
intersect line at 
. Let the circumcircles of 
and intersect again at 
(
). Let the lines 
intersect the circumcircle of 
again at 
(
). Prove that the lines 
concur.
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Incircle touch points are on circle
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Source: Kyiv Geometry O.
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Y by Adventure10, Mango247
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.
.
cut 
.
lay on perpendicular bisector of 
.
is diameter of 
.
.
touches it.
.
.
.
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Y by Adventure10, Mango247
Dear Mathlinkers,
see : http://jl.ayme.pagesperso-orange.fr/Docs/Quelques%20theoremes%20oublies.pdf
Sincerely
Jean-Louis
see : http://jl.ayme.pagesperso-orange.fr/Docs/Quelques%20theoremes%20oublies.pdf
Sincerely
Jean-Louis
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