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India STEMS
2024 India STEMS
STEMS 2024 Math Cat A
P3
P3
Part of
STEMS 2024 Math Cat A
Problems
(1)
AI_A and (S,SB) intersect at X, Y. prove that BCX = ACY
Source: STEMS 2024, CAT A, P3
12/17/2023
Let
A
B
C
ABC
A
BC
be a triangle. Let
I
I
I
be the Incenter of
A
B
C
ABC
A
BC
and
S
S
S
be the midpoint of arc
B
A
C
BAC
B
A
C
. Define
I
A
IA
I
A
as the
A
A
A
-excenter wrt
A
B
C
ABC
A
BC
. Define
ω
\omega
ω
to be the circle centred at
S
S
S
with radius
S
B
SB
SB
. Let
A
I
A
∩
ω
=
X
AI_A \cap \omega = X
A
I
A
∩
ω
=
X
,
Y
Y
Y
. Show that
∠
B
C
X
=
∠
A
C
Y
\angle BCX = \angle ACY
∠
BCX
=
∠
A
C
Y
.
geometry