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Posted

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

 

Posted

Your proof is not correct because it includes things like multiplying and dividing by infinity. It could probably be reworked in terms of limits to come up with a valid proof. 

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