similar-triangle-length-ratio
A length or area inside a synthetic plane figure is recovered by spotting a pair of similar triangles — created by parallel lines, tangent circles, a shared angle, or a right-angle altitude — and solving a single proportion (for a length) or applying the squared linear ratio (for an area). The decisive move is identifying the matched triangles and the correspondence of sides; there are no coordinates and no axis-aligned Pythagorean leg decomposition.
풀이 전략
- Swap a parallel-line cut for a tangent-circle configuration — the similarity argument changes from AA to SAS but the single-proportion finish is identical
- Ask for an area instead of a length to force the squared-ratio step (area scales as the square of the linear ratio)
- Change the given lengths so the scale_ratio stays clean (small rationals) while the surface figure looks different
세부 유형 분포 (2)
한 줄을 클릭하면 그 안의 문제를 볼 수 있어요.
- parallel-cut-area-ratio 7% (3)
One or more lines drawn parallel to the sides of a triangle cut off similar sub-triangles; the target region's area is read off as a difference of whole-triangle and sub-triangle areas, each obtained from the squared linear ratio of the parallel cut.
- synthetic-similarity-length 93% (43)
A synthetic configuration — tangent circles, a chord and its right triangles, or a rectangle diagonal with a perpendicular foot — produces a pair of similar triangles by SAS or shared-angle reasoning; a single proportion then yields the requested length, from which a triangle area may be computed.
no figureamc10-2002A-13no figureamc10-2002A-20no figureamc10-2002A-7
amc10-2004A-22no figureamc10-2004B-16
amc10-2004B-20no figureamc10-2004B-24no figureamc10-2005A-25
amc10-2006A-16
amc10-2006A-23
amc10-2006B-24no figureamc10-2007A-14no figureamc10-2007B-21no figureamc10-2007B-23no figureamc10-2008A-16
amc10-2009A-10no figureamc10-2009A-17
amc10-2009A-21no figureamc10-2009A-23no figureamc10-2009B-16no figureamc10-2009B-18
amc10-2009B-20no figureamc10-2010A-14no figureamc10-2010B-20no figureamc10-2011B-22
amc10-2011B-9no figureamc10-2012A-11
amc10-2013A-12no figureamc10-2013B-23no figureamc10-2013B-7no figureamc10-2014A-22no figureamc10-2014A-9
amc10-2014B-15no figureamc10-2015A-19
amc10-2015B-22no figureamc10-2016A-19no figureamc10-2016A-24no figureamc10-2017A-21no figureamc10-2017B-15no figureamc10-2017B-22
amc10-2018A-15
amc10-2025A-15no figureamc10-2025A-23
더 보기 (연도 추세, 도구 fingerprint, 학년 분포, 전체 문제)
도구 fingerprint (1–17)
학년 분포
- Gr 6 1
- Gr 7 2
- Gr 8 43