The area of the square is 100. What’s the missing length?pic.twitter.com/KQmN05dNRn
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Mathematical physicist and mentor to mathematically talented youth. Talent is that which bridges the gap between what can be taught and what must be learned.
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The area of the square is 100. What’s the missing length?pic.twitter.com/KQmN05dNRn
I found this result surprising - I had to check it several times to convince myself it was true. Did I just miss something obvious?
Easy check- When radius of small semi circle is zero, it becomes a point on right end of Dia of bigger semi circle.
Thanks - I think what I need convincing of most is that it will be invariant. Perhaps because my algebra was longer and messier than @nabadvin’s solution, so it all felt a bit like magic when a nice answer came out!
One way of looking at problems like this is that either they have no solution, or a single solution, independent of the arbitrary position of the undetermined element (in which case, a limiting argument almost always supplies the answer.) So it's a binary choice: one, or none.
Which is to say that if you're persuaded, despite the presence in the problem of an arbitrary element, that the information given is sufficient to determine *an* answer, then you're likewise persuaded that there can be *only one* answer. Even before you go looking for it.
That's the best approach for closed answer problems in some math contests, where you are given a multiple answer choice!
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