Sunday Times Teaser 2485
by Nick MacKinnon
Published: 9 May 2010 (link)
Jack and Kay  have inherited a circular field, with North Gate (N) at the northernmost point and East Gate (E), South Gate (S) and West Gate (W) at the appropriate points.
Jack’s share of the field is one hectare in area. For each point P in his share, three of the angles NPE, EPS, SPW and WPN are acute.
For each point in Katy’s  share, however, fewer than three of those angles are acute.
How far is it between North Gate and East Gate?
 There is a Sunday Times typographic error here – the intended name is is not known.