I’ve added a new Euclidean geometry handout, Constructing Diagrams, to my webpage.

Some of the stuff covered in this handout:

- Advice for constructing the triangle centers (hint: circumcenter goes first)
- An example of how to rearrange the conditions of a problem and draw a diagram out-of-order
- Some mechanical suggestions such as dealing with phantom points
- Some examples of computer-generated figures

Enjoy.

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Nice handout! The only suggestion I want to make is to remove point X in the geogebra diagram of that HMMT problems. It’s not in the problem’s statement and moreover it spoils the key point.

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I just want to add the following.

For those of us with worse rulers or who just suck at constructing perpendiculars, there’s an easier way to construct the orthocenter. Draw the A altitude and let it intersect BC at D and (ABC) at P. Then draw the circle with center D through P, and its other intersection with AD will be H (the orthocenter). This works because the reflection of H about BC lies on the circumcircle.

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