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Problems
Contests
National and Regional Contests
India Contests
India EGMO TST
India EGMO 2022 TST
3
3
Part of
India EGMO 2022 TST
Problems
(1)
Magical conditional geometry
Source: India EGMO 2022 TST P3
11/21/2021
Let
I
I
I
be incentre of scalene
△
A
B
C
\triangle ABC
△
A
BC
and let
L
L
L
be midpoint of arc
B
A
C
BAC
B
A
C
. Let
M
M
M
be midpoint of
B
C
BC
BC
and let the line through
M
M
M
parallel to
A
I
AI
A
I
intersect
L
I
LI
L
I
at point
P
P
P
. Let
Q
Q
Q
lie on
B
C
BC
BC
such that
P
Q
⊥
L
I
PQ\perp LI
PQ
⊥
L
I
. Let
S
S
S
be midpoint of
A
M
AM
A
M
and
T
T
T
be midpoint of
L
I
LI
L
I
. Prove that
I
S
⊥
B
C
IS\perp BC
I
S
⊥
BC
if and only if
A
Q
⊥
S
T
AQ\perp ST
A
Q
⊥
ST
.~Mahavir Gandhi