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18th Cabri Clubs 2007, round 1, level 2, 3 problems, Argentinian geo contest

Source:

December 8, 2021
geometrygeometric constructionconstructioncabri clubs

Problem Statement

level 2
p4. Let ABCDABCD be an isosceles trapezoid with bases ABAB and CDCD . It is known that ∠ABC=60o\angle ABC = 60^o, AB=6AB = 6 and BC=1BC = 1. Find the length of side CDCD and the area of ​​the trapezoid ABCDABCD. https://cdn.artofproblemsolving.com/attachments/6/d/79137a7d2428005454402b55adf23711c5dd8b.jpg
p5. There is a pentagon ABCDEABCDE such that: ∙\bullet ACEACE is an equilateral triangle. ∙\bullet AB=BC=CD=DEAB = BC = CD = DE ∙\bullet ∠ABC=∠CDE=120o\angle ABC = \angle CDE = 120^o a) Construct the figure. b) If AE=1AE = 1, find the length of BDBD.
p6. Let ABCDABCD be a parallelogram with AB=3AB = 3, BC=5BC = 5 and ∠ABC=60o\angle ABC = 60^o. Construct a parallelogram PQRSPQRS with P,Q,RP, Q, R and SS in AB,BC,CDAB, BC, CD and DADA, respectively, and that fulfills that PQ=2QRPQ = 2QR and ∠PQR=120o\angle PQR = 120^o.
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