@giraybudak1877
Easiest ayt question
@epsilonfox2593
First construct the 7-24-25 triangle by the Pythagorean Theorem. Denote by R the radius of the circle, R=sqrt(625-x²). By opposite angles supplementary, the quadrilateral with sides length 24,7,R,x is a cyclic quadrilateral. Then, by the Ptolemy's Theorem, 25*sqrt(625-x²)=7*sqrt(625-x²)+24x Hence x=15
@marioalb9726
Special right triangle 7-24-25 (2R)²=24²+(7+25)² --> R= 20cm x² = 25²-R² --> x= 15cm
@محمدحارثبھائی
The thing I loved the most is that all the values we encountered in the question are whole numbers. ❤️
@luyrian1280
in turkey this is just simple guy
@x.in_hype
Everytime i see this type of questions i remember Pythagorean theorem 😂
@sebggb5266
My solution: First, the four vertices of the square are called A, B, C, and D in clockwise order from the top. Then, BD = 25 (pythagorean). ∠BCD is 90°, so □ABCD is on a circle. (∠DAB + ∠BCD = 180°) As □ABCD is on a circle, AB×CD + BC×DA = AC×BD. then just substitute (radius of the fan = r) 7×r + x×24 = r×25 24x = 18r r = 4/3 x Now △BCD is a right triangle with 25, x, 4/3 x Use pythagorean, then x is 15.
@emirdemir465
A normal question in turkey exams
@Will-j6i6q
kinda feel sad for the comments tbh. if this is easy to you, congratulations. maybe this video isn't for you. a lot of us, including myself, is struggling with this type of question and that's why I'm here. seeing how you guys commented "oh this is nothing for us from here and there" or "this is 9th/10th grade type of question" is truly inconsiderate to those who are trying to learn. geez, sometimes being smart doesn't necessarily mean being humble
@arcticpilotshow4440
In my younger years I was very good at math, now I'm turning 60 and haven't used math much so I couldn't solve this. When I saw the solution I was a bit embarrassed. I have to re study this.
@PrashantSharma-c5x
I started to see Pythagoras theorem in my dreams😂😂
@Bonbonfito
La normal bir ayt sorusu 15 cevap ben de zor sorudur diye hevesle çözmeye başladım. 😢 20 saniyemi falan aldı güzel olmadı😢
@Avilass
The hardest part of this question is calculating whats square of 24 plus square of 32 without using pen and paper, in my mind. It comes pretty funny for turkish students that you think the question is hard.
@RobiyaMuhiddinova-h6c
Thanks 🎉
@matthieudutriaux
24^2+7^2=y^2+x^2 x^2=y^2+7^2-2*7*y*sqrt(1-((24/2)/y)^2) 625=y^2+x^2 x^2=y^2+7^2-2*7*y*sqrt(1-(12/y)^2) x^2=625-x^2+7^2-2*7*sqrt(625-x^2)*sqrt(1-144/(625-x^2)) answer : x=15
@RAG981
You missed using 3,4,5 triangle at the end (15,20,25) and earlier in the 24, 32, 40 one
@svkplayz
it was pretty easy
@bhoopathim5566
So goooooddddd
@bryanalexander1839
Set r² equations equal then 25²-x²=24²÷2²+32²÷2² so x²=25²-16²-12² x²=(25+16)(25-16)-12•12 x²=41•-9-12•9-12•3 x²=41•9-12•9-9•3-3•3 x²=(41-12-3-1)•9 x²=25•9 x=5•3 x=15 whatever units.
@eylulkorkmaz5776