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  • Two circles <img alt="\mathrm{x}^2+\mathrm{y}^2+2 \mathrm{~g}_{\mathrm{i}} \mathrm{x}+2 \mathrm{f}_{\mathrm{i}} \mathrm{y}+\mathrm{c}_{\mathrm{i}}=0, \mathrm{i}=1,2" src="https://entrancecorne

Two circles \mathrm{x}^2+\mathrm{y}^2+2 \mathrm{~g}_{\mathrm{i}} \mathrm{x}+2 \mathrm{f}_{\mathrm{i}} \mathrm{y}+\mathrm{c}_{\mathrm{i}}=0, \mathrm{i}=1,2 intersect at an angle of 120° as shown in the figure. Then \mathrm{\left(\mathrm{kg}_1 \mathrm{~g}_2+\mathrm{kf}_1 \mathrm{f}_2-\mathrm{c}_1-\mathrm{c}_2\right)^2=\left(\mathrm{g}_1^2+\mathrm{f}_1^2-\mathrm{c}_1\right)\left(\mathrm{g}_2^2+\mathrm{f}_2^2-\mathrm{c}_2\right)} where k=

 

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