Goat and circles

What is the radius of a circle centered on the other circle, and is the intersection of the two circles equal to half the area of the first circle?

This task is the mathematical expression of the role of agriculture. The farmer has circular land on which graze goats. Because the farmer wants to spend the grass throughout the two days, tie it to a stake on the edge of the circle and length of rope for the first half of the grass. The second day gives they a whole circle where they can feed off the remaining one-half of the grass.

Correct answer:

p=x/r =  116.9 %

Step-by-step explanation:

S1+S2=21S S=πr2 S1=21x2(αsinα) S2=21r2((2π2α)sin(2π2α))  x=2rcos(α/2)   α=tanα2cosαπ  α1=1.9056957293099=66°2325" p1=x/r=1.1587284730181=115.87% α2=4.0903294575997=52°2034" p2=x/r=0.91355336099303=91.36% α3=7.9263876105649=78°233" p3=x/r=1.3620993158089=136.21% α4=10.756961303274=70°4829" p4=x/r=1.235835638602=123.58% α5=11.0473869356=83°61" p5=x/r=1.4503719997774=145.04% α6=7.5128894066161=93°3618" p6=x/r=1.6337175982743=163.37% α7=4.8322830401789=85°4415" p7=x/r=1.49640036639=149.64%   

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