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2021 JBMO Shortlist
G2
G2
Part of
2021 JBMO Shortlist
Problems
(1)
JBMO Shortlist 2021 G2
Source: JBMO Shortlist 2021
7/2/2022
Let
P
P
P
be an interior point of the isosceles triangle
A
B
C
ABC
A
BC
with
A
^
=
9
0
∘
\hat{A} = 90^{\circ}
A
^
=
9
0
∘
. If
P
A
B
^
+
P
B
C
^
+
P
C
A
^
=
9
0
∘
,
\widehat{PAB} + \widehat{PBC} + \widehat{PCA} = 90^{\circ},
P
A
B
+
PBC
+
PC
A
=
9
0
∘
,
prove that
A
P
⊥
B
C
AP \perp BC
A
P
⊥
BC
.Proposed by Mehmet Akif Yıldız, Turkey
Junior
Balkan
shortlist
2021
geometry
arcs