Challenge Level

Simple hint: how would you find the set of points that are
equidistant from two given points?

When might that locus not intersect with the given line?

Harder, last part: try dropping perpendiculars from $A$ and $B$ onto the given line.

The distance between those positions might be useful.

When is $P$ between those positions and when is it outside?

When might that locus not intersect with the given line?

Harder, last part: try dropping perpendiculars from $A$ and $B$ onto the given line.

The distance between those positions might be useful.

When is $P$ between those positions and when is it outside?