Got it!
(At least I've convinced myself with a picture.)
Geometry was my weak point in competitions since we didn't do it much in school. I once successfully solved a competition problem using coordinates, and formed the false hope, despite warnings to the contrary, that this was the way to go. The warnings were right. Maybe
I need to take this course.
I never did either competitions or (much) geometry at school, and I learned a
lot from this course :-) Since DS's school maths teacher was sometimes letting him do these problems at school, I undertook to produce and send in a set of model answers each week, so that when DS was stuck the teacher didn't have to solve the problems in his head to help DS while also dealing with the rest of the class doing something completely different. It was more of an undertaking than I thought when I made it! (And it's both encouraging and probably good for school-home relations that the one time I had to confess I hadn't solved one of the problems yet, DS's teacher promptly sent me a solution!)
ETA yup, your solution is consistent with DS's (though my guess from the wording is that the method was not identical - there are several ways to approach this I think).
