Nine-point circle is a circle that contains the following nine points: midpoints of the sides of triangle ABC, feet of the altitudes of triangle ABC, and Euler points of the triangle
Euler points of a triangle are the midpoints of the segments joining the orthocenter of a triangle to its vertices. Orthocenter is the point of concurrency of the altitudes of a triangle. Altitude is the segment drawn from a vertex of the triangle perpendicular to the side opposite the vertex.
Drag any of the vertices of triangle ABC. Write down your observations as the triangle changes its size. And finally, how do you locate the center of this nine-point circle?
(Hint: What is a property of a perpendicular bisector of a chord in a circle that you can use in this case? Recreate the image on Geogebra to discover this property.)