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A triangle

Source: 2015 AMC 10B/12B #19

February 26, 2015
geometryperimeterAMC 10AMC

Problem Statement

In △ABC\triangle{ABC}, ∠C=90∘\angle{C} = 90^{\circ} and AB=12AB = 12. Squares ABXYABXY and ACWZACWZ are constructed outside of the triangle. The points X,Y,ZX, Y, Z, and WW lie on a circle. What is the perimeter of the triangle?
<spanclass=′latex−bold′>(A)</span> 12+93<spanclass=′latex−bold′>(B)</span> 18+63<spanclass=′latex−bold′>(C)</span> 12+122<spanclass=′latex−bold′>(D)</span> 30<spanclass=′latex−bold′>(E)</span> 32 <span class='latex-bold'>(A)</span>\ 12+9\sqrt{3}\qquad<span class='latex-bold'>(B)</span>\ 18+6\sqrt{3}\qquad<span class='latex-bold'>(C)</span>\ 12+12\sqrt{2}\qquad<span class='latex-bold'>(D)</span>\ 30\qquad<span class='latex-bold'>(E)</span>\ 32
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