I tried to coach the free tier of ChatGPT with words but couldn’t get it to solve. Was the reasoning model able to get it?

Details:

A lot of algebra for the extra credit but got a closed form expression for the extra credit:

Hi Zach - Just wanted to confirm: nearest part of the hose is not necessarily the perpendicular distance, right? I.e., can be an end point of the chord?

If I force-feed it the reasoning and just use (the free tier) it for evaluating the integrals individually it gets the answer pretty quick (much much faster than me). I guess still a huge productivity boost

This week’s fiddler: