17th Cabri Clubs 2002, round 1, level B, 4 problems, Argentinian geo contest
Source:
December 7, 2021
geometrycabri clubsgeometric constructionconstruction
Problem Statement
level B
p5. Construct the following figure formed by a square and two equilateral triangles and calculate the length of the segment knowing that .
https://cdn.artofproblemsolving.com/attachments/3/e/99cd1f1c5145e5f736f3cefcf41dae04f8b44e.gif
p6. Construct two equilateral triangles, so that the smaller one has one sixth of the area that the larger one has.
p7. Let be any triangle and the midpoint of . Construct a circle that passes through and is tangent to side at point .p8. If in the previous problem, the radius of the circle has length and the altitude from has length , find the length of and the possible measures of the angle where is the intersection of the circle with .