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2006 China Second Round Olympiad Test 1 #4

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September 28, 2014
geometry3D geometryprismanalytic geometrygraphing linesslope

Problem Statement

Given a right triangular prism A1B1C1−ABCA_1B_1C_1 - ABC with ∠BAC=π2\angle BAC = \frac{\pi}{2} and AB=AC=AA1AB = AC = AA_1, let GG, EE be the midpoints of A1B1A_1B_1, CC1CC_1 respectively, and DD, FF be variable points lying on segments ACAC, ABAB (not including endpoints) respectively. If GD⊥EFGD \bot EF, the range of the length of DFDF is <spanclass=′latex−bold′>(A)</span> [15,1)<spanclass=′latex−bold′>(B)</span> [15,2)<spanclass=′latex−bold′>(C)</span> [1,2)<spanclass=′latex−bold′>(D)</span>[12,2){ <span class='latex-bold'>(A)</span>\ [\frac{1}{\sqrt{5}}, 1)\qquad<span class='latex-bold'>(B)</span>\ [\frac{1}{5}, 2)\qquad<span class='latex-bold'>(C)</span>\ [1, \sqrt{2})\qquad<span class='latex-bold'>(D)</span>} [\frac{1}{\sqrt{2}}, \sqrt{2})\qquad
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