MathDB
Problems
Contests
National and Regional Contests
Poland Contests
Poland - Second Round
1999 Poland - Second Round
4
4
Part of
1999 Poland - Second Round
Problems
(1)
pair of equal angles given, right angle wanted, circumcenter related
Source: Polish second round 1999 p4
1/19/2020
Let
P
P
P
be a point inside a triangle
A
B
C
ABC
A
BC
such that
∠
P
A
B
=
∠
P
C
A
\angle PAB = \angle PCA
∠
P
A
B
=
∠
PC
A
and
∠
P
A
C
=
∠
P
B
A
\angle PAC = \angle PBA
∠
P
A
C
=
∠
PB
A
. If
O
≠
P
O \ne P
O
=
P
is the circumcenter of
△
A
B
C
\triangle ABC
△
A
BC
, prove that
∠
A
P
O
\angle APO
∠
A
PO
is right.
geometry
equal angles
right angle
Circumcenter