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

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

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

A_t=1/4[(4r²-c²)c²]^1/2

A_t=1/4[4r²c²-c⁴]^1/2

c=2Pi_*r / infinity

A_c= infinity_*A_t

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

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

A_c=Pi_*r²

A_t is triangle area

A_cis circle area

 

Do you mean like this
https://en.wikipedia.org/wiki/Area_of_a_circle#Rearrangement_proof

 

8 hours ago, John Cuthber said:

Do you mean like this
https://en.wikipedia.org/wiki/Area_of_a_circle#Rearrangement_proof

 

What is similar of those?

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.