Grades 11-12 Video Solutions 2021-video 2021 11-12/26

Video Transcription

Video Summary

The problem involves determining the number of unique triangles that can be formed by joining any three of 15 equally spaced points on a circle, where congruent triangles (by rotation or reflection) are considered the same. There are typically 455 ways to choose 3 points from 15 (using combinations), but many of these are congruent. By analyzing the shapes—5 equilateral, 6 unique isosceles, and 12 unique scalene triangles—and accounting for various congruences, the solution reveals there are 19 unique triangles that can be formed. Thus, the answer is 19 different triangles.