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Three reflections in an equilateral triangle

Source: Iran First Round 2018, P21

March 7, 2021
geometrygeometric transformationreflection

Problem Statement

The point PP is chosen inside or on the equilateral triangle ABCABC of side length 11. The reflection of PP with respect to ABAB is KK, the reflection of KK about BCBC is MM, and the reflection of MM with respect to ACAC is NN. What is the maximum length of NPNP?
<spanclass=′latex−bold′>(A)</span> 23<spanclass=′latex−bold′>(B)</span> 3<spanclass=′latex−bold′>(C)</span> 32<spanclass=′latex−bold′>(D)</span> 3<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>\ \frac{\sqrt 3}{2} \qquad<span class='latex-bold'>(D)</span>\ 3\qquad<span class='latex-bold'>(E)</span>\ 1
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