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15th Cabri Clubs 2001, round 1, level A, 5 problems, Argentinian geo contest

Source:

December 4, 2021
geometrycabri clubsconstructiongeometric construction

Problem Statement

level A
p1. Construct the following figure where ABCABC, CDECDE and FGHFGH are equilateral triangles, AEFHAEFH is a rectangle and AC=CE=EFAC = CE = EF.https://cdn.artofproblemsolving.com/attachments/f/b/5f39b1462b52f0404a6d73ef9343cfb8bb39f5.gif
p2. In the figure in problem 1, find the measure of segment BGBG.
p3. In the figure in problem 1, find the angle formed by lines BHBH and DFDF.
p4. Let ABCDABCD be a square, of area 3030. Let PP be a point on side ABAB such that 2AP=PB2 AP = PB. Let QQ be a point on side BCBC such that BQ=QCBQ = QC. Let RR be a point on side ADAD such that 2DR=RA2 DR = RA. Line PQPQ intersects line CDCD at MM and line PRPR intersects line CDCD at NN. Find the area of ​​the triangle MNPMNP.
p5. Given a square ABCDABCD, construct an isosceles triangle of equal area and with one side equal to the side of the square.
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