What is the radius? Gothic window puzzle

Can you solve this nice geometry problem? Special thanks this month to: Lee Redden, Mike Robertson, Daniel Lewis, Kyle. Thanks to all supporters on Patreon! / mindyourdecisions
problem
/ 1410621140775542786
solution
/ 1410641346445127682
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[@deerh2o]

Sweet problem and nicely solved.

[@TheMofRider2]

What an amazing solution! I knew the two arcs will come in handy, but had no idea it'll be that way to use them. Very nice.

[@philrobson4287]

It a bit of magic that the circle fits in so perfectly.

[@nexen1041]

Acquiring adequate knowledge in geometry theories helps a lot in solving such problems. It's all about basics

[@PratibhaBhadoriya-k2s]

Thanks

[@romnicklor9167]

Got it with the same solution.

[@jameshy69]

thanks man. always love the videos

[@ΚΑΝΑΒΟΣΜΑΝΩΛΗΣ]

Dear Sir, I have been following your posts regularly and have commented when deemed necessary. In my earlier comment if I remember correctly, I have made the same comment. that is, in this kind of problems, the major thing is not their solution, but the construction of the scheme, in order to make the solution. Here in particular, tell me in what way, having the compass and the rule, I will construct the tangent circles? Thanks for the hospitality.

[@lollol-tt3fx]

you can take that challenge on yourself as an additional puzzle but it is usually a lot easier to solve the lenghts and then contruct something, for example if someone wanted to make a pentagon with calssicall construction it would be very hard for him, had he nkt known the lenghts of the diagonals

[@joedarkmatter5051]

what a neat solution 🙏🏻

[@hvnterblack]

Good job! Thanks mate!

[@firstnamelastname307]

amazing property ! do you attribute the question to yourself ?

[@JohnDlugosz]

ChatGPT took 33 seconds (don't know if it's _hard_ or just server busy) and tells me: 6/5 units. Oh, and that's without any drawing; just the spoken text from the first minute.

[@barneynisbet6267]

Good geometry problem, with Pythag thrown in.

[@antoniopedrofalcaolopesmor6095]

Not difficult but fun to solve :)

[@castleanthrax1833]

Nothing is difficult if you know how to do it.

[@nickckckck]

@@castleanthrax1833what do you mean by that

[@castleanthrax1833]

@@nickckckck It's pretty self-explanatory, but I'll approach it from a different perspective; everything is easy when you know how to do it.

[@lollol-tt3fx]

your 2nd rwsponse is so funny​@@castleanthrax1833

[@leciniminis144]

who?

[@Imaspidah]

What is the formal reasoning behind claiming that AB is a radius?

[@AlecBrady]

It was specified in the construction

[@jameshy69]

BC and AC are arc segments centered around points A and B respectively. that's what the instructions said basically

[@Imaspidah]

thanks

[@verkuilb]

@0:08 “Construct the arc BC centered at A, and construct arc AC centered at B.”

[@robertloveless4938]

I thought the sane thing

[@sultanshihab3101]

thats so good

[@BhagyaRana]

Solved it! ✔

[@narangfamily7668]

Nifty!

[@reubenmanzo2054]

This is the main reason why I don't like circle geometry, it's a very polarising topic. You either take a single glance and see "A leads to B leads to C, there's your answer" or you'll be staring at it for half an hour and not a clue where to start.

[@derrickthewhite1]

I didn't remember "two tangent circles are colinear"... but I remembered that lines from the center to the circle are perpendicular to the tangent and that was enough.

[@Anti_Woke]

Proper job.

[@rootx2369]

is there any other way out there,however i have done by above method

[@krzysztof_jablonski]

By the looks of it I totally expected a transcendental or at least irrational result like e.g. √​​(π/2). 6/5 looks so plain...

[@robertloveless4938]

Cool

[@garrysekelli6776]

I was going to guestimate 1.2.

[@5alidshammout]

how did we know that A is the midpoint of the big circle?

[@Anmol_Sinha]

It was in the question. I am guessing you were watching with your phone muted 😅

[@theuppercutmac260]

It was mentioned at 0:05

[@yurenchu]

From the thumbnail: I'm assuming that the large arcs are circular arcs whose centers are at the bottom corners. Let r = unknown radius of the red circle M = center of the red circle T = top vertex A = bottom left vertex B = bottom right vertex C = midpoint of AB D = midpoint of AC S = point on arc BT where red circle touches BT. Since arc BT and the red circle _touch_ at S , we know that their radii AS and MS must be parallel; hence M is located _on_ AS. Furthermore, ACM and DCM are both right triangles with the right angle at C , and with side CM in common. Therefore (using Pythagorean Theorem), |CM|² = |AM|² - |AC|² |CM|² = |DM|² - |DC|² ==> |AM|² - |AC|² = |DM|² - |DC|² With |AM| = |AS| - r = (4 - r) , |AC| = 2 , |DM| = 1+r , |DC| = 1 , we'll have (4-r)² - 2² = (1+r)² - 1² Solving for r : 16 - 8r + r² - 4 = 1 + 2r + r² - 1 12 = 10r r = 12/10 = 1.2

[@derhausfreund5691]

Why r_0 = 1???

[@yajkrishna]

Is there a geometric solution?

[@Grizzly01-vr4pn]

The method presented in the video is purely geometric.

[@AlecBrady]

@@Grizzly01-vr4pnI think they meant “without algebra”. You could probably replicate all the algebra in pictorial form, with dissections of squares and such, but that would be a lot of faff for not much benefit.

[@dj_laundry_list]

I solved it using trig FML

[@user-sr5lw3bv9]

4-2√2

[@Sammmeow]

How the hell did i know the answer just by looking at the circles....

[@Nothingx303]

Νόστιμος 😊

[@youssefelyousfi4929]

r=6/5

[@ZEPHYRZHANG-mg8zi]

This does not seem hard to solve with using just algebra and turning everything into functions.

[@surgeonsergio6839]

Is it weird that I just guessed 1.2, without doing anything?

[@yurenchu]

Maybe it's a good day to buy a lottery ticket! 😊

[@Nengooo0]

เชิญ

[@raileite5994]

Early squad o/

[@pramodsingh7569]

Thanks