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15th Cabri Clubs 2001, round 1, level B, 4 problems, Argentinian geo contest

Source:

December 4, 2021
geometrygeometric constructionconstructioncabri clubs

Problem Statement

level B
p6. Let ABCDABCD be a parallelogram with ∠DAB\angle DAB acute. The bisector of ∠DBC\angle DBC intersects side CDCD at QQ and line ADAD at P. If AD=DPAD = DP, find the measure of angle ∠DQB\angle DQB.
p7. Construct the following figure formed by 44 circles of equal radius, tangent to each other and tangent to the sides of the parallelogram. https://cdn.artofproblemsolving.com/attachments/6/9/da7261850412b1277f331aa2e3c8bb6ceb5cf2.gif
p8. If in the previous problem the radius of the circles is 1cm, find the area of ​​the parallelogram.
p9. Given a square ABCDABCD, construct an isosceles triangle PQRPQR with the same perimeter as ABCDABCD and such that the base of PQRPQR measures half of the other two sides.
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