Problem 360. Area of a triangle, Curvilinear triangles, Circles,
Diameters.
Level: High School, College, SAT Prep.
In the figure below, ABC is an acute
triangle with area S. Circles of diameters AB, BC, and AC form
three curvilinear triangles of areas S_{1}, S_{2},
and S_{3}, respectively, and one internal curvilinear
triangle of area S_{4}.

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