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Rioplatense Mathematical Olympiad, Level 3
2014 Rioplatense Mathematical Olympiad, Level 3
5
5
Part of
2014 Rioplatense Mathematical Olympiad, Level 3
Problems
(1)
point B in segment AC, 3 circles of diameter AB,BC,AC
Source: Rioplatense Olympiad 2014 level 3 P5
9/4/2018
In the segment
A
C
A C
A
C
a point
B
B
B
is taken. Construct circles
T
1
,
T
2
T_1, T_2
T
1
,
T
2
and
T
3
T_3
T
3
of diameters
A
B
,
B
C
A B, BC
A
B
,
BC
and
A
C
AC
A
C
respectively. A line that passes through
B
B
B
cuts
T
3
T_3
T
3
in the points
P
P
P
and
Q
Q
Q
, and the circles
T
1
T_1
T
1
and
T
2
T_2
T
2
respectively at points
R
R
R
and
S
S
S
. Prove that
P
R
=
Q
S
PR = Q S
PR
=
QS
.
geometry
circles
diameter