Tag Archives: Geometry

[Soln] 2013 AIME I Problem 13

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

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2013 AIME I Problem 13

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

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[Soln] 2013 AIME I Problem 12

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

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2013 AIME I Problem 12

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

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[Soln] 2013 AIME I Problem 9

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

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2013 AIME I Problem 9

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

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[Soln] 2013 AIME I Problem 7

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

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