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1999 AMC 12 Question 21

AMC12 · 1999 AMC 12

Question 21

A circle is circumscribed about a triangle with sides $20,$ $21,$ and $29,$ thus dividing the interior of the circle into four regions. Let $A,$ $B,$ and $C$ be the areas of the non-triangular regions, with $C$ being the largest. Then
  1. $A + B = C$
  2. $A + B + 210 = C$
  3. $A^2 + B^2 = C^2$
  4. $20A + 21B = 29C$
  5. $\dfrac{1}{A^2} + \dfrac{1}{B^2} = \dfrac{1}{C^2}$