MathDB
Problems
Contests
National and Regional Contests
Spain Contests
pOMA and PErA mathematical olympiads
2023 pOMA
6
6
Part of
2023 pOMA
Problems
(1)
Config issues, you say?
Source: pOMA 2023/6
11/21/2023
Let
Ω
\Omega
Ω
be a circle, and let
A
A
A
,
B
B
B
,
C
C
C
,
D
D
D
and
K
K
K
be distinct points on it, in that order, and such that lines
B
C
BC
BC
and
A
D
AD
A
D
are parallel. Let
A
′
≠
A
A'\neq A
A
′
=
A
be a point on line
A
K
AK
A
K
such that
B
A
=
B
A
′
BA=BA'
B
A
=
B
A
′
. Similarly, let
C
′
≠
C
C'\neq C
C
′
=
C
be a point on line
C
K
CK
C
K
such that
D
C
=
D
C
′
DC=DC'
D
C
=
D
C
′
. Prove that segments
A
C
AC
A
C
and
A
′
C
′
A'C'
A
′
C
′
have the same length.
geometry
Angle Chasing