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National and Regional Contests
Argentina Contests
Argentina National Olympiad
2010 Argentina National Olympiad
2
2
Part of
2010 Argentina National Olympiad
Problems
(1)
computational with incircle of a right triangle, AP = QM
Source: 2010 Argentina OMA L3 p2
6/17/2020
Let
A
B
C
ABC
A
BC
be a triangle with
∠
C
=
9
0
o
\angle C = 90^o
∠
C
=
9
0
o
and
A
C
=
1
AC = 1
A
C
=
1
. The median
A
M
AM
A
M
intersects the incircle at the points
P
P
P
and
Q
Q
Q
, with
P
P
P
between
A
A
A
and
Q
Q
Q
, such that
A
P
=
Q
M
AP = QM
A
P
=
QM
. Find the length of
P
Q
PQ
PQ
.
geometry
incircle
right triangle