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Pan African
2017 Pan African
Problem 6
Problem 6
Part of
2017 Pan African
Problems
(1)
Problem 6 Midpoint of segment
Source: PAMO 2017 Problem 6
7/5/2017
Let
A
B
C
ABC
A
BC
be a triangle with
H
H
H
its orthocenter. The circle with diameter
[
A
C
]
[AC]
[
A
C
]
cuts the circumcircle of triangle
A
B
H
ABH
A
B
H
at
K
K
K
. Prove that the point of intersection of the lines
C
K
CK
C
K
and
B
H
BH
B
H
is the midpoint of the segment
[
B
H
]
[BH]
[
B
H
]
geometry
orthocenter
circumcircle