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at each point one can draw two rays tangent to F of angle of 60^o, locus

Source: Austrian Polish 1982 APMC

April 30, 2020

LocusTangentscircleconvexgeometry

Problem Statement

Let

F

be a closed convex region inside a circle

C

with center

O

and radius

1

. Furthermore, assume that from each point of

C

one can draw two rays tangent to

F

which form an angle of

60^o

. Prove that

F

is the disc centered at

O

with radius

1/2