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Sweden Contests
Swedish Mathematical Competition
1999 Swedish Mathematical Competition
2
2
Part of
1999 Swedish Mathematical Competition
Problems
(1)
<OPO' = 90^o wanted, externally tangent circles
Source: 1999 Swedish Mathematical Competition p2
4/2/2021
Circle
C
C
C
center
O
O
O
touches externally circle
C
′
C'
C
′
center
O
′
O'
O
′
. A line touches
C
C
C
at
A
A
A
and
C
′
C'
C
′
at
B
B
B
.
P
P
P
is the midpoint of
A
B
AB
A
B
. Show that
∠
O
P
O
′
=
9
0
o
\angle OPO' = 90^o
∠
OP
O
′
=
9
0
o
.
right angle
circles
geometry