MathDB
Turkey NMO 2000 1st Round - P01 (Geometry)

Source:

July 24, 2012
geometrycircumcircleinradius

Problem Statement

If the incircle of a right triangle with area aa is the circumcircle of a right triangle with area bb, what is the minimum value of ab\frac{a}{b}?
<spanclass=latexbold>(A)</span> 3+22<spanclass=latexbold>(B)</span> 1+2<spanclass=latexbold>(C)</span> 22<spanclass=latexbold>(D)</span> 2+3<spanclass=latexbold>(E)</span> 23 <span class='latex-bold'>(A)</span>\ 3 + 2\sqrt2 \qquad<span class='latex-bold'>(B)</span>\ 1+\sqrt2 \qquad<span class='latex-bold'>(C)</span>\ 2\sqrt2 \qquad<span class='latex-bold'>(D)</span>\ 2+\sqrt3 \qquad<span class='latex-bold'>(E)</span>\ 2\sqrt3