>>124689
how is the line calculated? this is too much of a sketch to do anything concrete with

>>124689
paint it fully red, then cut it into 1cm wide strips, cut off all the not-red parts and puzzle it together. now you can just measure how long the strip it. it's not exact but who gives a fuck, your teacher is a whore and that's good enough for a whore.

>>124691
I know for a fact it can be done. There is a square, a circle and another line that you can construct using a compass.
I don't know how exactly, though. So here would be my actions:
1. Call friend who is getting a phd in mathematics.
2. Describe the problem.
3. Calculate using his instructions.
4. Profit.

>>124689
use integral calculus
protip: a circle centered in (0,0) with radius r has formula y = ±√(r²-x²)

>>124700
ok
I think it's easiest in this coordinate system
the smaller circle has centre in (0,0) and radius 5
5² = y² + x²
or
y = ±√(5² - x²)
the larger circle (well, just the arc) has centre in (0,-5√2) and radius 10
10² = (y + 5√2)² + x²
or
y = ±√(10² - x²) - 5√2
(the first is implicit formula and the second in explicit formula; in both cases only the +√ branch of the explicit formula, the one in upper semiplane, is relevant)
the circles intersect in points where x² is the same in both implicit formulas:
5² - y² = 10² - (y + 5√2)²
(y + 5√2)² - y² = 10² - 5²
y² + 10√2y + 50 - y² = 75
10√2y = 25
y = 5/2√2
calculating x of intersections:
5² = y² + x²
25 = 25/8 + x²
x² = 25(7/8)
x = ±5√7/2√2
now you want to integrate between those intersections (from -x to x) the difference between integrals of both circles' explicit formulas:
ʃ √(5² - x²) dx - ʃ √(10² - x²) - 5√2 dx
indefinite integral of √(r² - x²) you can find in integral tables;
(fuck this is getting ugly. you get the idea. if you can't solve it from here on, maybe I go come return and finish it tomorrow. good night bernd.group)
(protip: you can integrate only from 0 to x since shape is symmetric, total area is twice that)

>>124709
and i only got as far as figuring out that those ares are equal

>>124719
ok well tone'd
guess I don't have to finish it myself

>>124723
I got afraid when I opened the integral tables and saw arctans

>>124729
Ssb = small box area
Ssc = small circle area
Sbb = big box area
Sbc = big circle area
4Ssb = Sbb
4Ssc = Sbc
a + b + c + d = Ssb
a + b = Ssb - Ssc
c + d = Sbc / 4 = 4Ssc / 4 = Ssc
b + c = Ssc
c + d = b + c
d = b

>>124738
oh I see, it's simple
the idea is that the small circle has same area as that quarter big circle
everything follows straightforwarldy