UK Maths Challenge | Shortcuts For Finding Greatest or Least

This is a great problem from Q25 of the UK Intermediate Maths Challenge 2000 that the official solution to doesn't capture a very neat time-saving trick.
When comparing, you don't always need to work out the absolute value of each, only to show that one exceeds the other. This is similar to how we tackle problems in the real world, problems that usually call for choosing between constrained options rather than calculating in the abstract.
Try to write your own that combines arithmetic and geometry and leave your thoughts below.
#ukmc #ukmaths #ukmt #mathschallenge #maths #math #amcmath #artofproblemsolving #geometry #gcse #alevel

[@gerryiles3925]

You can use the same "flipping over a copy" argument, but with the 4 shaded segments, you used for B for the last one to show it must be less than half of the circle.

[@eternity_hour]

You're right, I didn't fully my own advice and use the same trick. Thanks for pointing that out

[@normanklein3155]

This seems to be one of those questions, where it's just not really worth knowing the answer to it. As the answer doesn't really lead to any greater knowledge, except for answering stupid questions on tests.