Tag Archives: Geometry

2013 AIME I 13. Triangle has side lengths , , . For each positive integer , points  and are located on  and  respectively, creating three similar triangles . The area of the union of all triangles  for  can be expressed as , where  and  are relatively prime … Continue reading →

2013 AIME I 13. Triangle has side lengths , , . For each positive integer , points  and are located on  and  respectively, creating three similar triangles . The area of the union of all triangles  for  can be expressed as , where  and  are relatively prime … Continue reading →

2013 AIME I 12. Let  be a triangle with  and . A regular hexagon  with side length 1 is drawn inside  so that side  lies on , side  lies on , and one of the remaining vertices lies on . There are … Continue reading →

2013 AIME I 12. Let  be a triangle with  and . A regular hexagon  with side length 1 is drawn inside  so that side  lies on , side  lies on , and one of the remaining vertices lies on . There are … Continue reading →

2013 AIME I 9. A paper equilateral triangle  has side length 12. The paper triangle is folded so that vertex  touches a point on side a distance 9 from point . The length of the line segment along which the triangle is folded … Continue reading →

2013 AIME I 9. A paper equilateral triangle  has side length 12. The paper triangle is folded so that vertex  touches a point on side a distance 9 from point . The length of the line segment along which the triangle is folded … Continue reading →

2013 AIME I 7. A rectangular box has width 12 inches, length 16 inches, and height  inches, where  and are relatively prime positive integers. Three faces of the box meet at a corner of the box. The center points of those three faces … Continue reading →

2013 AIME I 7. A rectangular box has width 12 inches, length 16 inches, and height  inches, where  and are relatively prime positive integers. Three faces of the box meet at a corner of the box. The center points of those three faces … Continue reading →

2013 AIME I 3. Let be a square, and let  and  be points on  and , respectively. The line through  parallel to  and the line through  parallel to  divide into two squares and two non-square rectangles. The sum of the areas of … Continue reading →