MathDB
Problems
Contests
National and Regional Contests
Chile Contests
Chile TST Ibero
2024 Chile TST Ibero.
5
5
Part of
2024 Chile TST Ibero.
Problems
(1)
You know how to draw?
Source:
10/22/2024
Let
△
A
B
C
\triangle ABC
△
A
BC
be an acute-angled triangle. Let
P
P
P
be the midpoint of
B
C
BC
BC
, and
K
K
K
the foot of the altitude from
A
A
A
to side
B
C
BC
BC
. Let
D
D
D
be a point on segment
A
P
AP
A
P
such that
∠
B
D
C
=
9
0
∘
\angle BDC = 90^\circ
∠
B
D
C
=
9
0
∘
. Let
E
E
E
be the second point of intersection of line
B
C
BC
BC
with the circumcircle of
△
A
D
K
\triangle ADK
△
A
DK
. Let
F
F
F
be the second point of intersection of line
A
E
AE
A
E
with the circumcircle of
△
A
B
C
\triangle ABC
△
A
BC
. Prove that
∠
A
F
D
=
9
0
∘
\angle AFD = 90^\circ
∠
A
F
D
=
9
0
∘
.
TST
Chile
geometry