Question

Define Nine Point Centre of a triangle with diagram.​

Answer 1

Answer:

The nine-point center is the circumcenter of the medial triangle of the given triangle, the circumcenter of the orthic triangle of the given triangle, and the circumcenter of the Euler triangle. The nine-point center lies at the centroid of four points: the triangle's three vertices and its orthocenter.

Answer 2

Nine-point Circle

The nine-point circle of a triangle is a circle going through 9 key points:

the three midpoints of the sides of the triangle (blue in the below picture),

the three feet of the altitudes of the triangle (yellow in the below picture), and

the three midpoints from the vertices to the orthocenter of the triangle (green in the below picture).

The nine-point circle satisfies several important and interesting properties, besides the surprising fact that it exists at all.

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