Geometry · Rectangle · Circular sector · Arc length · Equilateral triangle · Area by subtraction
A rectangle \(ABCD\) satisfies \(|AB| = 10\) and \(|AC| = 5\sqrt{7}\). Let \(M\) be the midpoint of the side \(AB\). Inside the rectangle we draw the semicircle with diameter \(AB\) and the triangle \(CDM\), and then shade the part of the triangle that lies outside the semicircle, as in the figure. Compute the perimeter and the area of the shaded figure.
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Slovenian High School Mathematics Competition for Vega Awards (MaSSA), odbirno (qualifying) round 2024, 1. letnik, category A, problem 2. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source