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Switzerland Contests
Switzerland Team Selection Test
2000 Switzerland Team Selection Test
9
9
Part of
2000 Switzerland Team Selection Test
Problems
(1)
a segment construction, passing through intersections of two circles
Source: Switzerland - Swiss TST 2000 p9
2/19/2020
Two given circles
k
1
k_1
k
1
and
k
2
k_2
k
2
intersect at points
P
P
P
and
Q
Q
Q
. Construct a segment
A
B
AB
A
B
through
P
P
P
with the endpoints at
k
1
k_1
k
1
and
k
2
k_2
k
2
for which
A
P
⋅
P
B
AP \cdot PB
A
P
⋅
PB
is maximal.
intersecting circles
geometric construction
construction
geometry
Segment
max