'99 Percent' Miss This. What Is The Radius?

What is the radius of the circle, in simplest terms involving a, b, and c? I read that even the great mind Richard Feynman made a mistake. Watch the video to learn the common mistake and what the correct answer is.

Source Feynman story

My blog post for this video

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Connect with me

[Tahgtahv]

To b, or not to b?, that is the question (and the answer). (But not 2b, that'd be the diameter).

[mithical]

I feel smart. Thank you, Fresh Skywalker.

[skoockum]

"A common mistake is to use the Pythagorean Theorem."

D'oh!

[tropicocean]

I guess
r = b+0ac
as it has to be in terms off a, b, c.

[GretgorPooper]

I was really pissed off when I realized the solution. Thankfully, I managed to see it for myself, cuz if I had to watch the solution, I'd be really salty.

[reda.kharoubi]

b right?
the first time i actually got the right answer in 5 seconds

[jasonpatterson]

The answer seemed so straightforward that I wound up proving it in 3 different ways before I believed that I hadn't screwed up...

[QuippersUnited]

Oh man, this is the sort of problem that tries to console you by suggesting that common folk like me might be on the same level of Richard Feynman since in his massive career of brilliance, he happened to brainfart on ONE easy problem. It's the intellectual equivalent of telling an 11 year old child that "everybody wets the bed at some point in their life."

[rubencuneo]

The trick is in the premise: find the simplest formula for r in term of "a, b and c". The proposed solution indicates r=b, but what about a and c? May be it´s foolish, but that what can be seen as well

[JaelinBai]

In terms of just a and c the answer is:


r = a + c + sqrt(2ac)


I got that by substituting the r with b in the 'incorrect' answer and manipulating it to isolate b.

[problematicpuzzlechannel]

This type of problem we tend to overthink lol

[acarbonbasedlifeform]

I solved it very quickly (the same way as you showed), didn't believe myself, tried to disprove this solution and couldn't do it. I'm very happy that I figured it out myself. Thanks Presh for your hard work and teaching us to think independently and outside the box!

[ahmedslama]

I figured it is 'b' at first but thought that"oh no, it isn't that freakn simple man, this isn't ordinary maths"

[fernandox]

I did it but then i thought "it says in terms of a, b, c"

[mattIbg]

I discovered this channel few days ago and whatched a lot of videos, this is the first that I was able to solve. There's still hope!

[sangeetamankani]

1st time, I was able to get the right answer on my own!!

[vishytheprof]

Cool... I thought of extending the analysis. If we equate both these values of r and solve the equation; we get the following result:::
b = a+c+sqrt(2ac) or
b = a+c-sqrt(2ac)

Hope this makes sense!
Cheers

[roderickwhitehead]

i was like "Um? r=b?" wondering what the "Gotcha" was.

[nicholasbermel]

Something to note is that it is never given that the corner of the rectangle meets at a single point with the arc. It is defined as being a right angle, but nothing is given other than visual assumption that they meet. So, while we assume that r = the radius of the quarter circle, we also have to assume that the rectangle intersects at the arc and only at 1 point.

[anandk]

I managed to solve this within couple of minutes or so. But I'll definitely admit that it's not obvious to consider that concept to get to the answer. It's indeed a fooling question.

Loved it a lot!! Love you, Presh Talwalkar and your mind blowing 'Mind your decisions' creation !!! 😄