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Part of 2000 National Olympiad First Round

Problems(1)

Turkey NMO 2000 1st Round - P01 (Geometry)

Source:

7/24/2012
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=′latex−bold′>(A)</span> 3+22<spanclass=′latex−bold′>(B)</span> 1+2<spanclass=′latex−bold′>(C)</span> 22<spanclass=′latex−bold′>(D)</span> 2+3<spanclass=′latex−bold′>(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
geometrycircumcircleinradius