This is the [url=http://en.wikipedia.org/wiki/Nine-point_circle]nine point circle[/url]. The nine point circle is a circle which appears in any triangle, made up of midpoints and intersections of perpendicular lines that cross through points.[br][br]Instructions for its creation are [url=http://jwilson.coe.uga.edu/EMT668/EMT668.Folders.F97/Anderson/geometry/geometry1project/construction/construction.html]here[/url], and simplified [url=http://tube.geogebra.org/student/m718999]here[/url].[br][br]The black lines are construction of the points, the orange lines are construction of the circle's centre.[br][br]Drag the dots A, B, C to change the size and shape of the triangle.

[list=1][br][*] Find the relation between [b]the positions of the lines and dots[/b] and [b]the type of triangle[/b] (e.g. right-angled, equilateral, isosceles)[br][*] Construct the nine point triangle using the instructions [url=http://jwilson.coe.uga.edu/EMT668/EMT668.Folders.F97/Anderson/geometry/geometry1project/construction/construction.html]here[/url].[br][/list]