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1996 Cabri Clubs 1st, Round 1, 6 problems, Argentinian geo contest

Source:

November 25, 2021
geometrycabri clubsconstructiongeometric construction

Problem Statement

level 1
p1. Construct the following rhombus: https://cdn.artofproblemsolving.com/attachments/6/e/51994ddfd1246fadeb64c62f75e24ca14e8980.gif
p2. Given a triangle ABCABC, construct a triangle whose area is 1/61/6 of that triangle ABCABC.
p3. Given a segment ACAC and a line ℓ\ell, find a point BB on the line ℓ\ell such that ∠ABC=60o\angle ABC=60^o.
level 2
p4. Construct the following figure : https://cdn.artofproblemsolving.com/attachments/8/1/484c34ef009cb2230cfb4ef66edfc1f39936db.gif
p5. Given a triangle ABCABC, construct a hexagon that has the same area as ABCABC.
p6. Given two non intersecting circles C1C_1 and C2C_2, such that neither is exterior to the other, find points EE and GG on C1C_1 and FF on C2C_2 such that the measure of the angle ∠EFG\angle EFG is maximum.
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