MathDB
Problems
Contests
International Contests
Baltic Way
2022 Baltic Way
12
12
Part of
2022 Baltic Way
Problems
(1)
Two circles passing through a point on the altitude
Source: Baltic Way 2022/12
11/12/2022
An acute-angled triangle
A
B
C
ABC
A
BC
has altitudes
A
D
,
B
E
AD, BE
A
D
,
BE
and
C
F
CF
CF
. Let
Q
Q
Q
be an interior point of the segment
A
D
AD
A
D
, and let the circumcircles of the triangles
Q
D
F
QDF
Q
D
F
and
Q
D
E
QDE
Q
D
E
meet the line
B
C
BC
BC
again at points
X
X
X
and
Y
Y
Y
, respectively. Prove that
B
X
=
C
Y
BX = CY
BX
=
C
Y
.
geometry