### What is an Orthocenter, and how do I construct this
last triangle?

by
### Julia Neal

The **orthocenter** is the point of concurrency
of the three altitudes of a triangle.

The third triangle is created by finding the
orthocenter of our original triangle. The midponts of the segments
whose endpoints are the orthocenter and the vertices of the original
triangle form the vertices of this triangle.

This is our original triangle. The first step
is to find the **orthocenter**. To do this, we need to find
the altitude of each side. The **altitude** is the perpendicular
segment drawn from the vertex of a triangle to the line containing
the opposite side of the triangle.

The dashed blue lines are our altitudes. Notice
that they meet at a single point. This point is the **orthocenter**.
Next we need to find the midpoints of the segments that connect
the vertices with the orthocenter.

Those midpoints will be the the vertices of
our new triangle. We need to connect the midpoints to draw the
triangle.

This blue triangle is the third triangle
that helps form the 9 point circle. Its endpoints are 3 of the
9 points.

**return to 9 point circle page**

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