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Belgium Contests
Flanders Math Olympiad
2022 Flanders Math Olympiad
1
1
Part of
2022 Flanders Math Olympiad
Problems
(1)
equal angles wanted, intersecting chords
Source: 2022 VWO Flanders MO p1
11/17/2022
The points
A
,
B
,
C
,
D
A, B, C, D
A
,
B
,
C
,
D
lie in that order on a circle. The segments
A
C
AC
A
C
and
B
D
BD
B
D
intersect at the point
P
P
P
. The point
B
′
B'
B
′
lies on the line
A
B
AB
A
B
such that
A
A
A
is between
B
B
B
and
B
′
B'
B
′
and
∣
A
B
′
∣
=
∣
D
P
∣
|AB'| = |DP |
∣
A
B
′
∣
=
∣
D
P
∣
. The point
C
′
C'
C
′
lies on the line
C
D
CD
C
D
such that
D
D
D
is between
C
C
C
and
C
′
C'
C
′
lies and
∣
D
C
′
∣
=
∣
A
P
∣
|DC' | = |AP|
∣
D
C
′
∣
=
∣
A
P
∣
. Prove that
∠
B
′
P
C
′
=
∠
A
B
D
′
\angle B'PC' = \angle ABD'
∠
B
′
P
C
′
=
∠
A
B
D
′
.https://cdn.artofproblemsolving.com/attachments/2/2/7ec65246ff5ecfebc25ca13f3709d1791ceb6c.png =
geometry
equal angles