Question

Draw an acute scalene triangle △ ???. Construct its nine-point circle.

Answer 1

To construct the nine point circle of a triangle, follow these steps.

1. Draw a triangle ABC.

2. Construct the midpoints of the three sides. Label them as L, M, N.

3. Construct the feet of the altitudes of the triangle ABC. Label them as D, E, F. Label the point of intersection of the three altitudes as H. This is also called the orthocenter.

4. Construct the midpoints of the segments AH, BH, CH. Label them as X, Y, Z.

First, notice the nine points, L,M,N,D,E,F,X,Y, Z, lie in a circle.

This circle is called the Nine-Point Circle.