Circumcircle of a Triangle
Source:
January 11, 2009
geometrycircumcircle
Problem Statement
A circle is circumscribed about a triangle with sides , , and , thus dividing the interior of the circle into four regions. Let , , and be the areas of the non-triangular regions, with 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}