Assignment 4

by

Allison McNeece

**Medial triangle: **

Constructing any triangle and then find the mid points of the sides. Connect these points to form a smaller triangle inside the original triangle. This smaller triangle is the medial triangle.

Here is one for you to play with. Click and drag any vertice to explore how the medial triangle changes:

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medial triangle

**Orthic Triangle: **

Construct any acute triangle. From each angle, construct a line that is perpindicular to the opposite side. The points where these lines intersect the sides are the vertices of the orthic triangle.

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When does the orthic triangle disappear?

**Orthocenter-Midsegment Triangle: **

Construct any triangle and find the orthocenter. Then construct segments from the orthocenter to each vertex. Find the midpoints of these segments and connect them to form the orthocenter-midsegment triangle.

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When is orthocenter-midsegment triangle outside of the larger triangle?

**All together now:**

Now let's put it all together and observe each triangles circumcenter:

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hmmmm.... they all have the same circumcenter

Since they all have the same circumcenter it follows that they all have the same circumcircle

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This is the 9-point circle.

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