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Rioplatense L-A 2022 #5

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December 13, 2022
geometryperimeter

Problem Statement

The quadrilateral ABCDABCD has the following equality ∠ABC=∠BCD=150∘\angle ABC=\angle BCD=150^{\circ}. Moreover, AB=18AB=18 and BC=24BC=24, the equilateral triangles △APB,△BQC,△CRD\triangle APB,\triangle BQC,\triangle CRD are drawn outside the quadrilateral. If P(X)P(X) is the perimeter of the polygon XX, then the following equality is true P(APQRD)=P(ABCD)+32P(APQRD)=P(ABCD)+32. Determine the length of the side CDCD.
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