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New Zealand Contests
NZMOC Camp Selection Problems
2018 NZMOC Camp Selection Problems
4
4
Part of
2018 NZMOC Camp Selection Problems
Problems
(1)
<PXY=90^o wanted, <CPA=90^o, <CBP=<CAP, midpoints (2018 NZOMC Camp Sel. p4)
Source:
1/10/2021
Let
P
P
P
be a point inside triangle
A
B
C
ABC
A
BC
such that
∠
C
P
A
=
9
0
o
\angle CPA = 90^o
∠
CP
A
=
9
0
o
and
∠
C
B
P
=
∠
C
A
P
\angle CBP = \angle CAP
∠
CBP
=
∠
C
A
P
. Prove that
∠
P
X
Y
=
9
0
o
\angle P XY = 90^o
∠
PX
Y
=
9
0
o
, where
X
X
X
and
Y
Y
Y
are the midpoints of
A
B
AB
A
B
and
A
C
AC
A
C
respectively.
geometry
right angle
equal angles