MathDB
Turkey NMO 2008 1st Round - P21 (Geometry)

Source:

August 26, 2012
geometryangle bisector

Problem Statement

Let ABCABC be a right triangle with m(A^)=90m(\widehat{A})=90^\circ. Let APQRAPQR be a square with area 99 such that P[AC]P\in [AC], Q[BC]Q\in [BC], R[AB]R\in [AB]. Let KLMNKLMN be a square with area 88 such that N,K[BC]N,K\in [BC], M[AB]M\in [AB], and L[AC]L\in [AC]. What is AB+AC|AB|+|AC|?
<spanclass=latexbold>(A)</span> 8<spanclass=latexbold>(B)</span> 10<spanclass=latexbold>(C)</span> 12<spanclass=latexbold>(D)</span> 14<spanclass=latexbold>(E)</span> 16 <span class='latex-bold'>(A)</span>\ 8 \qquad<span class='latex-bold'>(B)</span>\ 10 \qquad<span class='latex-bold'>(C)</span>\ 12 \qquad<span class='latex-bold'>(D)</span>\ 14 \qquad<span class='latex-bold'>(E)</span>\ 16