MathDB
Problems
Contests
National and Regional Contests
Ukraine Contests
Random Geometry Problems from Ukrainian Contests
Kharkiv City MO Seniors - geometry
2012.11.4
2012.11.4
Part of
Kharkiv City MO Seniors - geometry
Problems
(1)
parallel wanted, incircle related (Kharkiv City XI 2012 - Ukr)
Source:
3/10/2020
The incircle
ω
\omega
ω
of triangle
A
B
C
ABC
A
BC
touches its sides
B
C
,
C
A
BC, CA
BC
,
C
A
and
A
B
AB
A
B
at points
D
,
E
D, E
D
,
E
and
E
E
E
, respectively. Point
G
G
G
lies on circle
ω
\omega
ω
in such a way that
F
G
FG
FG
is a diameter. Lines
E
G
EG
EG
and
F
D
FD
F
D
intersect at point
H
H
H
. Prove that
A
B
∥
C
H
AB \parallel CH
A
B
∥
C
H
.
geometry
parallel
incircle
Kharkiv