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P17 [Geometry] - Turkish NMO 1st Round - 2004

Source:

November 12, 2013
geometrytrigonometryLaTeX

Problem Statement

Let RR and TT be points respectively on sides [BC][BC] and [CD][CD] of a square ABCDABCD with side length 66 such that ∣CR∣+∣RT∣+∣TC∣=12|CR|+|RT|+|TC|=12. What is tan⁡(RAT^)\tan (\widehat{RAT})
<spanclass=′latex−bold′>(A)</span> 23<spanclass=′latex−bold′>(B)</span> 3<spanclass=′latex−bold′>(C)</span> 13<spanclass=′latex−bold′>(D)</span> 12<spanclass=′latex−bold′>(E)</span> 1 <span class='latex-bold'>(A)</span>\ 2\sqrt 3 \qquad<span class='latex-bold'>(B)</span>\ \sqrt 3 \qquad<span class='latex-bold'>(C)</span>\ \dfrac 13 \qquad<span class='latex-bold'>(D)</span>\ \dfrac 12 \qquad<span class='latex-bold'>(E)</span>\ 1
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