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National and Regional Contests
Serbia Contests
Serbia Team Selection Test
1973 Yugoslav Team Selection Test
Problem 2
Problem 2
Part of
1973 Yugoslav Team Selection Test
Problems
(1)
given point, find diameter
Source: Yugoslav TST 1973 P2
5/30/2021
A circle
k
k
k
is drawn using a given disc (e.g. a coin). A point
A
A
A
is chosen on
k
k
k
. Using just the given disc, determine the point
B
B
B
on
k
k
k
so that
A
B
AB
A
B
is a diameter of
k
k
k
. (You are allowed to choose an arbitrary point in one of the drawn circles, and using the given disc it is possible to construct either of the two circles that passes through the points at a distance that is smaller than the radius of the circle.)
geometry
construction