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doi:10.1016/0097-3165(92)90094-B 
Copyright © 1992 Published by Elsevier Inc.
Repeated angles in the plane and related problems*1
Received 13 February 1990.
Communicated by the Managing Editors
Available online 7 September 2004.
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Abstract
We show that a set of n points in the plane determine O(n2 log n) triples that define the same angle α, and that for many angles α (including π/2) this bound is tight in the worst case. We also show that, for a broad family of properties
, the number of triangles spanned by the given points and having property
is O(n7/3). Typical such properties are: having a specified area, a specified perimeter, being isosceles, etc.
