Area Challange!

[@edsznyter1437]

Angle AGC is 120, so it subtends 1/3 of the disc. Trangle ACG is easy.
N[3^2*Pi/3 - 3/2* Sqrt[3]*3/2] =~ 5.52766.
Avoids trig.

[@GeoSolve]

Nice catch. Thanks for the comment👍

[@pluto9000]

Yes but why do you need the area? Is it something to do with planting seeds?

[@GeoSolve]

It is for a 1.65MW solar power plant.

[@zdrastvutye]

there is 2 times a repeated calculation to avoid 2nd degree equations:
10 print "geosolve-area challange!":dim x(2),y(2):nu=29
20 r1=3:xm1=r1:ym1=0:r2=2:xm2=2*r1-r2:ym2=0:sw=r2/(r1+r2):xa=0:ya=0
30 n=r1^2+r2^2:xd=xm2-r2:goto 60
40 yd=ym2+sqr(r2^2-(xd-xm2)^2):dgu1=(xa-xd)*(xm2-xd)/n:dgu2=(ya-yd)*(ym2-yd)/n
50 dg=dgu1+dgu2:return
60 gosub 40
70 dg1=dg:xd1=xd:xd=xd+sw:xd2=xd:gosub 40:if dg1*dg>0 then 70
80 xd=(xd1+xd2)/2:gosub 40:if dg1*dg>0 then xd1=xd else xd2=xd
90 if abs(dg)>1E-10 then 80:rem die schnittpunkte berechnen
100 xc=sw:goto 130
110 dyc=(yd-ya)/(xd-xa)*(xc-xa):yc=ya+dyc:dgu1=(xc-xm1)^2/n:dgu2=(yc-ym1)^2/n
120 dgu3=r1^2/n:dg=dgu1+dgu2-dgu3:return
130 gosub 110
140 dg1=dg:xc1=xc:xc=xc+sw:xc2=xc:gosub 110:if dg1*dg>0 then 140
150 xc=(xc1+xc2)/2:gosub 110:if dg1*dg>0 then xc1=xc else xc2=xc
160 if abs(dg)>1E-10 then 150
170 x(0)=0:y(0)=0:x(1)=xm2:y(1)=ym2:x(2)=xc:y(2)=yc:masx=1200/2/r1:masy=900/r1
180 if masx

[@GeoSolve]

Thanks for sharing your solution.

[@zdrastvutye]

ich würde mit einem thales kreis anfangen, um die schnittpunkte zu berechnen

[@GeoSolve]

I'll start learning German👍

[@MathFinalBoss]

Helllo. I am the guy who sent a problem that I couldn't solve about 2 week sago. Have you got some idea?

[@GeoSolve]

Hi, I didn't have the time for that.