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Is the circle area proof correct?


DimaMazin

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Circle is shared by infinite quantity of equal triangles.  Sides a and b are radiuses of the circle.  Side c is chord,

At=1/4[(a+b+c)(-a+b+c)(a-b+c)(a+b-c)]1/2

At=1/4[(2r+c)(c)(c)(2r-c)]1/2

At=1/4[(4r2-c2)c2]1/2

At=1/4[4r2c2-c4]1/2

c=2Pi*r / infinity

Ac= infinity*At

Ac=(1/4)*infinity[4r24Pi2r2 / infinity2-16Pi4r4 / infinity4]1/2

Ac=1/4[16Pi2r4-16Pi4r4 / infinity2]1/2

Ac=Pi*r2

At is triangle area

Acis circle area

 

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