Paula Whitmire

Assignment 8

Altitudes and Orthocenters

 

Triangle BCD below has orthocenter L constructed from the intersection of the three lines containing the altitudes. The altitudes are perpendicular segments from the vertices to the opposite sides.

Now we will find the orthocenter of triangle LDC.

The orthocenter will be point B.

 

Now we will find the orthocenter of triangle BLD. The orthocenter will be point C.

Now we will find the orthocenter of triangle BLC and it is point D.

 

Now we construct the circumcenter of triangle BCD. It is point T.

 

Now we construct the circumcircle of triangle BCD with center T.

After much investigating, it was determined that the circumcenters for the smaller triangles was outside this triangle. Plus it is very late. Thanks again Dr. Wilson, I never dreamed I would learn so much.

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