Small challenge

[Pekis]

Hello,

I just don't fully understand the figure in your cone challenge ...

Anyway, I wanted to give an epilogue to my challenge with a generalized formula with a isosceles triangle (with one base and two equal sides) instead of an equilateral one:

let c=Fraction of Outer circle radius left for the isosceles triangle
let p=1-c=Fraction of Outer circle radius for the figure inside the inner circle
let b=Base length of the isosceles triangle
let e=Fraction of the outer circle radius for base length => b=e*r
let d=Side length of the isosceles triangle
let a=Fraction of the outer circle radius for side length => d=a*r
let k=a/e=Ratio between Side and Base of the isosceles triangle

=> a=(sqrt(4*k²-p²)-p*sqrt(4*k²-1))/(2*k)
It's good looking ...

Arc length: r*2*arcsin(a/(2*k))
Arc height: r*sqrt(4-(a/k)²)/2
Arc Angle span: 2*arcsin(a/(2*k))
Arc Start angle: t+arcsin(a/(2*k))
Arc End angle: t-arcsin(a/(2*k))
And instead of the PI/6 angle in ACE, we now have Angle ACE=arcsin(1/(2*k))

For an equilateral triangle, k=1 and it leads to
a=((sqrt(4-p²)-p*sqrt(3))/2
(same as previous formula a=(sqrt(3)*(c-1)+sqrt((c+1)*(3-c)))/2))

Thanks