The perpendicular bisectors of AB and AC intersect at D. [br][br]If you drag the point A to the right (or left), how will D move in this figure? Make a guess before you drag A.

A quick silent video below shows this construction and how to drag the points in the way suggested above. [br][br]Note how we may "trace" the point D to facilitate investigation and discussion.

Alex Bellos suggests an interesting paper folding experiment in his book, which also allows similar exploration ([url=https://www.evernote.com/shard/s3/sh/77b8bc36-9544-449a-9d67-205d3049ac76/6544ac082e3d0423e5fc0be2c8f91757]see my note[/url]).