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Australian AMC 2021 - Senior Question 23

AMC AUSTRALIA · Australian AMC 2021 - Senior

Question 23

Sebastien has a square paper serviette of side 24 cm. He folds it along a diagonal to form triangle $ABC$, right-angled at $A$. He then folds $C$ onto a point $D$ on $AB$; this fold meets $BC$ at $X$. He next folds $B$ onto $X$, and this new fold passes through $D$. What is the distance $AD$, in centimetres?
  1. $6\sqrt2$
  2. $12(\sqrt3-1)$
  3. 10
  4. 12
  5. $24(\sqrt2-1)$