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Geometry Puzzle: What’s the Radius?

Education

In this math video I (Susanne) explain how to solve this geometry puzzle, where we have a large square containing a smaller square and a circle. The circle and the inner square touch each other at the center of the circle. Using the Pythagorean theorem and a bit of algebra, we find the radius of the circle step by step. This video is perfect for anyone studying geometry, preparing for math exams, or just loves solving interesting math problems. Mathematics explained. 00:00 Intro – Geometry Puzzle 1:02 How to solve this 3:57 Diagonal Square 6:55 Finding x 10:27 Solving the Equation 12:27 See you later! *My German Math Channel:* ​⁠ @MathemaTrick *Find me on Instagram:* https://www.instagram.com/mathema_trick *Buy Me a Cup of Hot Chocolate?* ☕🍫 Creating these math tutorials takes a lot of brainpower and a warm cup of hot chocolate always helps! If you'd like to support my work and keep the tutorials coming, consider treating me to a virtual cup. 👉 https://paypal.me/TheMathQueen Thank you so much for your kindness! It means the world to me! #puzzle #maths #mathematics

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thomastempest62 2 months ago

The way you teach is exceptional. 👏👏👏

thibaultpixel54
thibaultpixel54 2 months ago

I used to watch your channel in German, my children don't know any German and I am happy that you have an English channel now. The way to go.

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georgesnight77 2 months, 2 weeks ago

Very nice. Thank you.

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danielleadams340 3 months, 1 week ago

Great, very clear method of teaching

sarah_wallace
sarah_wallace 4 months ago

You're in depth and intriguing. It's good to follow along.

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grégoire_louis 4 months, 1 week ago

Such a wonderful lesson! Thank you Suzanne! ❤

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allenanderson404 4 months, 3 weeks ago

brilliant again !! you are terrific

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brianmartin440 4 months, 4 weeks ago

Thank you for finally posting one I could do without cheating!!!

keith_davis
keith_davis 5 months ago

Simplest : First let's call the four corners of the big sqaure A (Up Left), B (Up Right), C (Bottom Left) and D (Bottom Right). Then I divided the big square into 4 small squares. Then I focus on the corner down right of the big square point D. Take the bottom horizontal side of the square (''C'' to ''D''). Length is 4. Separate it in two parts : on the left (corner bottom left point ''C'') you have first a segment that is the length of the circle radius (r) and in the right, you have the rest of the square bottom side which is the tangeant from point D. Now you take the second tangeant of the circle from point D, which goes from D to the center of the image. This tengeant is the hypothenuse of the small square down right. WHich is the square root of 8 = 2.83. So both tengeant from D are 2.83 long. Then to the bottom tangeant you add ''r'' to make the full length of the bottom side of the big square (4). So r = 4 - 2.83 = 1.17. Simple as that. Made in 30 seconds instead of 12:33 (LOL).

sarah_wallace
sarah_wallace 5 months, 1 week ago

Finally I could solve it on my own 😊

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garytaylor19 5 months, 2 weeks ago

You should sell a book of these puzzles. Very fun

micheal_santiago
micheal_santiago 5 months, 2 weeks ago

You present math in a lovely manner. Intuitively I assumed the result to be around 1. Had to hang to the end to find out.

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sarah.zuniga 5 months, 2 weeks ago

So beautiful problem math queen. Yes I solved it.

christine_woods
christine_woods 5 months, 2 weeks ago

subscribed... clearly i need to review the fundamentals. I had all the right ideas, but not the last few steps. Thanks!

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adán.cuellar 5 months, 3 weeks ago

The diagonal is 4√2, so half of it is 2√2. If you draw the second diagonal, you will see that it is tangent to the circle and meets it exactly at a length of 2√2. The other tangent has the same length, so the bottom side can be divided into two segments: r + 2√2 = 4. Therefore, the result is r = 4 - 2√2. Your longer solution stops before the final simplification; just multiply the denominator by √2 - 1 to complete it. Thank you for making math feel engaging and enjoyable to follow.

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cheyenne_brown 5 months, 3 weeks ago

Thanks for the review

michael.campbell
michael.campbell 5 months, 4 weeks ago

Mechanical engineer here and I went through a lot of math in my life, but nothing was so elegant as you solving problems…

angela.patterson
angela.patterson 6 months ago

It's so simple when you explain it. Thanks.

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vincent_webb 6 months ago

Great job🎉

kabir_khalsa
kabir_khalsa 6 months, 2 weeks ago

Clearly one of the best channels on YouTube._