Very Tricky Geometry Challenge | Find the side length of the square

[@shaurya12321]

Beautiful bro! Keep it up ! I m following u from past 2 yrs n I m suggesting everyone to see ur vids. Even my sis!

[@MathBooster]

Thank you so much 😀

[@MarieAnne.]

This is the solution I got. Nicely explained. Interestingly, when x = (9−√33)/2 we get a square ABCD that covers part of bottom left quadrant of circle, with line BD tangent to the arc of circle contained in that square.

[@holyshit922]

I focused on triangle EAD Compared two formulas for area of this triangle 1/2*((x-1)+x+y)*2 = 1/2*(x-1)*x From Pythagorean theorem i got y^2 = (x-1)^2+x^2 After squaring both sides of equation 1/2*((x-1)+x+y)*2 = 1/2*(x-1)*x i get quartic equation easy to factor but squaring both sides introduce some extraneous solutions

[@shaurya12321]

EAD?

[@alexniklas8777]

x=(9+√33)/2

[@raymondfrey9465]

Did anyone else get the annexation of Puerto Rico as the answer???