cusp

A sharp point or pointed end.

An important moment when a decision is made that will determine future events.

Newcastle were 11 points adrift of Spurs following their 5-0 mauling at the hands of the north London club in February. But a sixth successive Premier League win puts them on the cusp of European football next season as they surged 15 points clear of seventh-placed Everton, who have five games left to play.

A point of a curve where the curve is continuous but has no derivative, but such that it has a derivative at every nearby point.

A point made by the intersection of two curved lines or curved structures, a common motif in Gothic architecture.

A boundary between zodiacal signs and houses.

To behave in a reckless or dangerous manner.