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2022 New Zealand MO
7
7
Part of
2022 New Zealand MO
Problems
(1)
perpendicular bisector of BC bisects segment AD
Source: 2022 NZMO - New Zealand Maths Olympiad Round 1 p7
10/9/2022
Let
M
M
M
be the midpoint of side
B
C
BC
BC
of acute triangle
A
B
C
ABC
A
BC
. The circle centered at
M
M
M
passing through
A
A
A
intersects the lines
A
B
AB
A
B
and
A
C
AC
A
C
again at
P
P
P
and
Q
Q
Q
, respectively. The tangents to this circle at
P
P
P
and
Q
Q
Q
meet at
D
D
D
. Prove that the perpendicular bisector of
B
C
BC
BC
bisects segment
A
D
AD
A
D
.
geometry
bisects segment