Excel Investigation: Ring on a String

Age 11 to 16 Challenge Level:

The investigation offered this month is called Ring on a String, and uses Excel to optimise a characteristic of interest (minimise a length in this case).

The ring R is free to run along the taut string AB.

A second string passes through this ring and is pulled tight, before each end is attached to a peg in the two lines of pegs.

Each line of pegs is perpendicular to AB, as shown in the diagram below.

Ring on string
Using a spreadsheet, determine the position taken by R as the positions of C and D vary.

You will have to make some decisions about start values for this investigation.

For example: how long will you make AB, and what different positions of C and D will you explore?