9 point circle

 One if tge beautiful result in geometry is 9 point circle. We all know that given any three non-collinear  points we can always draw a circle which passes through those 3 points and if given 4 random points the chances are pretty slim that we can find a circle which will pass through all 4 points and so its pretty amazing that we can draw 9 points and find a circle which passes through all those 9 points. The following construction I did for my grade 7 students and it illustrates the idea of 9 point circle. First start with any triangle its better if its an acute angled one (but it doesn't matter).  The breakdown of these 9 points are
3 points which are the mid points of the sides of the triangle
3 points which are the foot of the altitudes
3 points are the mid points between orthocenter and the vertex of the triangle