C.a.R. > Applications > Similarity and Angles> Chord Tangent Theorem

This is a trisection by folding. Start with any angle with the blue point. Then move the point below, such that the paper corner is on the first parallel line. The folded end of the second parallel must be on the angle, which is automatic here.

Why does this work?

Technical Information

The only problem is to keep the second endpoint on the angle.