There is no escape...believe it or not. Mathematics is everywhere.
I would not ask the answer. I would ask them to create a mathematical representation of the problem.
As result they should be speaking about "circle" and "rectangle" and not about "spotlight" and "duct tape".
Then, they should solve the abstract representation.
Then go back to the original situation.
I would ask to clearly separate the 3 steps. That way I could see what is wrong in their development.
I suggest deleting the horizontal measurements from the Spotlight diagram, and setting it as a problem. What are the lengths L1, L2 and L3 of each piece of tape and what percentage of the area of the circle is covered? It can be solved with the aid of GeoGebra, which has a toolbar function to calculate the length of each piece of tape (distance between intersection points), or by solving the equations for the points on a circle, using the equation x^2+y^2=r^2, with r=85 and y2=48/2 for the long piece of tape and y1=48/2+48 for the short pieces of tape. L1=L3=2*x1, L2=2*x2. The SVG and image files for these examples are available for download in the Box.Net panel on my 24x7.ning.com profile page: I created Spotlight.svg with the free Inkscape drawing package. I place these examples in the public domain. (My blog on Vox.com is published under a Creative Commons Attribution-Share Alike License.)