Angles of Intersecting Chords
Here's a problem based on an obscure theorem about angles of intersecting chords.
Combined Chords
Two circles intersect at P and Q. Let’s call line AB through P a combined chord if AP and PB are chords of the respective circles. Let’s define the split product of AB as the length of AP times the length of PB.
Chord-bisecting Chords
A circle of radius 5 has chord AB with length 6. A second chord is drawn here and is bisected by AB.