Brilliant Geometry Puzzle

[themathhatter]

Never even heard of the intersecting chords theorem. What a lovely, niche tool to have in one's back pocket.

[Insightfill]

3:26 "That is... elegant." Gotta agree.. When I saw that coming together I thought "wait a minute..."

[lelonhere]

I really like all these effects you do with the squares and such.
The level of detail is amazing as well! Like completing the texture on squares that aren't fully visible in the original photo.

[matthieudutriaux]

Andy's method (with secant chords theorem) is the quickest then the smartest one.

Here is a less brilliant method :
a : side length of yellow square
b : side length of orange square
c : side length of red square
d : side length of green square
x : radius of the semi-circle

Equation 1 : a=sqrt(18)=3*sqrt(2)
Equation 2 : b+d=a=3*sqrt(2)
Equation 3 : sqrt(x^2-d^2)=d+sqrt(x^2-c^2) ; (particular vertex of green and red squares are in the semi-circle)
Equation 4 : ; (particular vertex of green and orange squares are in the semi-circle)

a, b, c, d, x are 5 unknowns and we have 4 equations.
We can not determine all of the 5 unknowns : a, b, c, d, x but we will see that we can determine : area=a^2+b^2+c^2+d^2

area=a^2+b^2+c^2+d^2
area=a^2+(b+d)^2-2*b*d+c^2
area=a^2+a^2-2*b*d+c^2
area=18+18+c^2-2*b*d
area=36+c^2-2*b*d

Equation 4 :






(thanks to Equation 2)


3*sqrt(2)-d=sqrt(x^2-d^2)
b=sqrt(x^2-d^2) ; x^2=b^2+d^2

Equation 3 :
sqrt(x^2-d^2)=d+sqrt(x^2-c^2)
b=d+sqrt(x^2-c^2) (thanks to Equation 4)
(b-d)^2=x^2-c^2
b^2+d^2-2*b*d=x^2-c^2
x^2-2*b*d=x^2-c^2
c^2-2*b*d=0

area=36+c^2-2*b*d
area=36

[Midnightspirit]

you should do some more calculus videos

[bestutubever]

DUDE your videos cure my brainrot love your approaches

[scouris]

Wow, your solution really snuck up there! Was not expecting it to be that easy. Love your work!

[randomrandom]

Oooh first time I hear about the Intersecting Chords Theorem. Good to know. Thank You.

[justinvance]

Oh my gosh! I was so sure this would finally be the video where you just troll us and say, "The answer is inconclusive. There is not enough information." Even though it uses pretty simple concepts, I don't know if I could have ever figured it out on my own. Did anybody?

[tiedye]

Can do tgis without any algebra: basically pick sized for the inner squares at the edge cases, if tge green square is of zero legth thab the red square is of zero length and the orange square matches the yellow, thus the size is 2*18=36

[JordanBiserkov]

So a^2 = b^2 + c^2 + d^2 means that the area of the green, red and orange squares equal the area of the yellow square, regardless of any numbers, this feels much deeper than 36 sq units.

[avantesma]

Oh, boy.
Catriona Agg and Andy Math.
It's one of those nights.
Oh, boy. 😊

[mikel]

The fact that the circle is there tells me I probably have to use it in some way, but given i don’t remember anything about chord theorems, is there another way using algebra and ratios? There’s gotta be no?

[tjelol]

just make equal lines until everything is equally lined and very simply do some basic addition
nvm the square behind must have a triangle shape by that thing

Obrigado por incendiares os meus neurónios!... 😀 How exciting!

[carmicha]

All of these Katerina problems are great.

[Quizlz]

So basically, because only one measurement was given, the image was almost perfectly proportional, so I eyeballed it and guessed 36 and was pleasantly surprised it was right.

[happystoat]

I failed to complete it but I started with :
(c + d) ^ 2 + d^2 = c^2
c + 2d = sqrt(18)
There is a way to continue and solve from there without the intersecting chord theorem, right?

[Tdragonfly]

I’m terrible with math but I have a crush so I watch😂

[doovstoover]

Ok as usual my brain was clinging on my its fingernails so I probably misunderstood something obvious... but in order for the intersecting chords thing to work, don't we have to assume that the corners of the squares are touching the edge of the semicircle?