Circles and squares are two common geometric shapes encountered very often in our daily life. In this series we present a class of fun problems involving circles in a square.<\/p>\n\n\n\n
Look at the following figure, a quarter circle is drawn inside a unit square. \n![\"\"](\"wp-content\/uploads\/2020\/10\/Screen-Shot-2019-11-19-at-10.39.04-PM.png\")
\nLet $[XY…Z]$ denote the area of the region with vertices of $X$, $Y$, \u2026, $Z$. The area of the region bounded by line $\\overline{AB}$, $\\overline{AD}$ and arc $\\stackrel\\frown{BD}$ is $$[ABD] = [ABCD]\\ -\\ [BCD] = 1\\ -\\ \\frac{\\pi}{4}$$<\/p>\n\n\n\n
In the following figure, another quarter circle is drawn: ![\"\"](\"wp-content\/uploads\/2020\/10\/Screen-Shot-2019-11-19-at-10.41.28-PM.png\")
\nThe area of the region bounded by two arcs with end points as $B$ and $D$ is: $$[BDB] = 1\\ -\\ 2 \\cdot [ABD] = 1\\ -\\ 2 \\cdot (1\\ -\\ \\frac{\\pi}{4}) = \\frac{\\pi}{2}\\ -\\ 1$$<\/p>\n\n\n\n\n
To be continued…<\/em><\/p>\n","protected":false},"excerpt":{"rendered":" Circles and squares are two common geometric shapes encountered very often in our daily life. In this series we present a class of fun problems involving circles in a square. Look at the following figure, a quarter circle is drawn inside a … Continue reading