MathDB

21

Part of 1999 AMC 12/AHSME

Problems(1)

Circumcircle of a Triangle

Source:

1/11/2009
A circle is circumscribed about a triangle with sides 20 20, 21 21, and 29 29, thus dividing the interior of the circle into four regions. Let A A, B B, and C C be the areas of the non-triangular regions, with C C being the largest. Then (A)\ A \plus{} B \equal{} C\qquad (B)\ A \plus{} B \plus{} 210 \equal{} C\qquad (C)\ A^2 \plus{} B^2 \equal{} C^2\qquad \\ (D)\ 20A \plus{} 21B \equal{} 29C\qquad (E)\ \frac{1}{A^2} \plus{} \frac{1}{B^2} \equal{} \frac{1}{C^2}
geometrycircumcircle