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2022 A Individual #16

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April 28, 2022
2022 A Individualgeometry

Problem Statement

Let PP be a point on side AB‾\overline{AB} of equilateral triangle ABCABC. If BP=6BP = 6 and CP=9CP = 9, what is the length of ABAB?
<spanclass=′latex−bold′>(A)</span>25<spanclass=′latex−bold′>(B)</span>3+6<spanclass=′latex−bold′>(C)</span>35<spanclass=′latex−bold′>(D)</span>36+3<spanclass=′latex−bold′>(E)</span>62<span class='latex-bold'>(A) </span>2\sqrt5\qquad<span class='latex-bold'>(B) </span>3+\sqrt6\qquad<span class='latex-bold'>(C) </span>3\sqrt5\qquad<span class='latex-bold'>(D) </span>3\sqrt6 + 3\qquad<span class='latex-bold'>(E) </span>6\sqrt2
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