MathDB
Problems
Contests
National and Regional Contests
Latvia Contests
Latvia BW TST
2021 Latvia Baltic Way TST
P11
P11
Part of
2021 Latvia Baltic Way TST
Problems
(1)
Incentre with perpendicularity
Source: Latvia BW TST 2021 P11
9/26/2021
Incircle of
△
A
B
C
\triangle ABC
△
A
BC
has centre
I
I
I
and touches sides
A
C
,
A
B
AC, AB
A
C
,
A
B
at
E
,
F
E,F
E
,
F
, respectively. The perpendicular bisector of segment
A
I
AI
A
I
intersects side
A
C
AC
A
C
at
P
P
P
. On side
A
B
AB
A
B
a point
Q
Q
Q
is chosen so that
Q
I
⊥
F
P
QI \perp FP
Q
I
⊥
FP
. Prove that
E
Q
⊥
A
B
EQ \perp AB
EQ
⊥
A
B
.
geometry
incenter
perpendicular bisector