MathDB
17th Cabri Clubs 2002, round 1, level C, 4 problems, Argentinian geo contest

Source:

December 7, 2021
geometryconstructiongeometric constructioncabri clubs

Problem Statement

level C
p9. For the pentagon ABCDEABCDE, we know that: ∙\bullet AB = 10cm ∙\bullet BC = 12cm ∙\bullet CD = 15cm ∙\bullet EA = 12cm. ∙\bullet Also, the angles B,CB, C, and EE of the pentagon are right. Find the area of ​​the pentagon.
p10. Given three points MM, DD and EE, construct a triangle ABCABC such that: Let MM be the midpoint of BCBC. Let DD be the foot of the altitude from AA Let EE be the foot of the altitude from BB
p11. Construct the following figure where: https://cdn.artofproblemsolving.com/attachments/a/1/6155e642acd25e339fba51ad02c2d5e543199f.gif ∙\bullet AD=CDAD = CD and AE=EBAE = EB ∙\bullet ∠CDB=45o\angle CDB = 45^o and ∠EBC=60o\angle EBC = 60^o
p12. Let ABCABC be an equilateral triangle with side kk and let S1S_1, S2S_2 and S3S_3 be the circles of radius kk and centers A,BA, B and CC respectively. Let XX be the point of intersection between S1S_1 and S2S_2 (other than CC). Let YY be the point of intersection of S2S_2 and S3S_3 (other than AA). Let ZZ be the point of intersection of S3S_3 and S1S_1 (other than BB). Let PP be a point in S1S_1. Draw the line PXPX that intersects S2S_2 at QQ. Draw the line QYQY that intersect S3S_3 at RR and draw the line RZRZ that intersect S1S_1 at TT. Prove that PTPT is a diameter of S1S_1.
Back to ProblemsView on AoPS