MathDB
Problems
Contests
National and Regional Contests
Turkey Contests
Turkey Junior National Olympiad
2019 Turkey Junior National Olympiad
3
3
Part of
2019 Turkey Junior National Olympiad
Problems
(1)
Geometry about incircle
Source: Turkey Junior Math Olympiad 2019 #3
12/23/2019
In
A
B
C
ABC
A
BC
triangle
I
I
I
is incenter and incircle of
A
B
C
ABC
A
BC
tangents to
B
C
,
A
C
,
A
B
BC,AC,AB
BC
,
A
C
,
A
B
at
D
,
E
,
F
D,E,F
D
,
E
,
F
, respectively. If
A
I
AI
A
I
intersects
D
E
DE
D
E
and
D
F
DF
D
F
at
P
P
P
and
Q
Q
Q
, prove that the circumcenter of
D
P
Q
DPQ
D
PQ
triangle is the midpoint of
B
C
BC
BC
.
geometry
geometry proposed
incenter
circumcircle