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P29 [Geometry] - Turkish NMO 1st Round - 2003

Source:

May 31, 2014
geometrycircumcircleincenter

Problem Statement

In right triangle ABCABC, let DD be the midpoint of hypotenuse [AB][AB], circumradius be 52\dfrac 52 and ∣BC∣=3|BC|=3. What is the distance between circumcenter of △ACD\triangle ACD and incenter of △BCD\triangle BCD?
<spanclass=′latex−bold′>(A)</span> 292<spanclass=′latex−bold′>(B)</span> 3<spanclass=′latex−bold′>(C)</span> 52<spanclass=′latex−bold′>(D)</span> 53412<spanclass=′latex−bold′>(E)</span> 22 <span class='latex-bold'>(A)</span>\ \dfrac {29}{2} \qquad<span class='latex-bold'>(B)</span>\ 3 \qquad<span class='latex-bold'>(C)</span>\ \dfrac 52 \qquad<span class='latex-bold'>(D)</span>\ \dfrac{5\sqrt{34}}{12} \qquad<span class='latex-bold'>(E)</span>\ 2\sqrt 2
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