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# 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

## 2013 AIME I Problem 13

## [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

## 2013 AIME I Problem 12

## [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

## 2013 AIME I Problem 9

## [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