Geometry · Pythagorean theorem · Perpendicular lines · Quadrilaterals · Sum of squares identity
In the convex quadrilateral \(ABCD\) the line through \(A\) and \(D\) and the line through \(B\) and \(C\) meet at a right angle, as the figure shows. Furthermore \(|CD| = 1\), \(|AC| = 2\) and \(|BD| = 3\). How long is \(AB\)?
- A \(2\sqrt{3}\)
- B \(3\sqrt{2}\)
- C \(4\)
- D \(4\sqrt{3}\)
- E \(6\)
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Slovenian High School Mathematics Competition for Vega Awards (MaSSA), drzavno (national) round 2017, 1. letnik, category A, problem A1. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source