I am given three co-ordinate points of a circle O(Ox,Oy) as a center. Then two Points other points as A(Ax,Ay) &amp; B(Bx,By). Now I have to find the arc length of that circle. Can you please help. Thanks in advance.

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I am given three co-ordinate points of a circle O(Ox,Oy) as a center. Then two Points other points as A(Ax,Ay) &amp;amp; B(Bx,By). Now I have to find the arc length of that circle. Can you please help. Thanks in advance.

Rhett Pruitt · Accepted Answer

We know the radius of the circle is   O  A  =      (          A      x        −          O      x              )      2        +    (          A      y        −          O      y              )      2       We can also find   A  B  =      (          A      x        −          B      x              )      2        +    (          A      y        −          B      y              )      2      . Since we know OA, OB (which is simply OA) and AB, we can find   ∠  A  O  B using the Cosine Rule. Once we have   ∠  O  A  B, then the arc length ACB is equal to:            ∠      A      O      B              360              ∘              ⋅  2  π  ⋅  O  AEDIT:To obtain   ∠  A  O  B, we know that by Cosine Rule:  c  o  s  ∠  A  O  B  =            A              B        2            −      O              A        2            −      O              B        2              2  Thus   ∠  A  O  B  =  c  o      s          −      1        (            A              B        2            −      O              A        2            −      O              B        2              2    )

I am given three co-ordinate points of a circle O(Ox,Oy)

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