Y by GeoKing, SBYT
1. I is incenter of triangle
.
is the midpoint of arc
not containing
.
is the midpoint of arc
is the midpoint of
and
is the midpoint of
.
is projection of
onto
.
is the second intersection of
and 
Prove that
is tangent to
.
2. Circle
with center
is incircle of triangle
.
is projection of
onto
Points
on segments
,
are following condition:
.
is the midpoint of
.
is the second intersection of
and
.
is the second intersection of
and
.
Prove, that
are concyclic.
I am grateful to Savva Chuev for making the diagrams.
















Prove that


2. Circle


















Prove, that

I am grateful to Savva Chuev for making the diagrams.
This post has been edited 2 times. Last edited by NT_G, Dec 31, 2023, 1:18 PM