Geometry · Inscribed circle · Area ratio · Scaling · Square grid
The squares \(ABCD\) and \(EFGH\) both have side \(1\). The first is cut into nine congruent small squares and the second into sixteen congruent small squares; in every small square the inscribed circle is drawn, and all these circles are shaded, as in the figure. What is the ratio of the shaded area of \(ABCD\) to the shaded area of \(EFGH\)?
- A \(\dfrac{9}{16}\)
- B \(\dfrac{3}{4}\)
- C \(1\)
- D \(\dfrac{4}{3}\)
- E \(\dfrac{16}{9}\)
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Slovenian High School Mathematics Competition for Vega Awards (MaSSA), regijsko (regional) round 2011, 1. letnik, category A, problem A1. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source