MathDB
Problems
Contests
National and Regional Contests
USA Contests
USA - High School Proof Olympiads
Ersatz MO (USEMO)
2024 USEMO
3
3
Part of
2024 USEMO
Problems
(1)
X56 Jumpscare
Source: USEMO 2024/3
10/26/2024
Let
A
B
C
ABC
A
BC
be a triangle with incenter
I
I
I
. Two distinct points
P
P
P
and
Q
Q
Q
are chosen on the circumcircle of
A
B
C
ABC
A
BC
such that
∠
A
P
I
=
∠
A
Q
I
=
4
5
∘
.
\angle API = \angle AQI = 45^\circ.
∠
A
P
I
=
∠
A
Q
I
=
4
5
∘
.
Lines
P
Q
PQ
PQ
and
B
C
BC
BC
meet at
S
S
S
. Let
H
H
H
denote the foot of the altitude from
A
A
A
to
B
C
BC
BC
. Prove that
∠
A
H
I
=
∠
I
S
H
\angle AHI = \angle ISH
∠
A
H
I
=
∠
I
S
H
.Matsvei Zorka
geometry
USEMO
USEMO 2024