Grades 11-12 Video Solutions 2024-2024_11-12

Video Transcription

Video Summary

Twelve points are evenly spaced on a circle. We aim to determine how many triangles containing a 45-degree angle can be formed. A 45-degree angle can be formed by two points that are 90 degrees apart. For each pair of such points, there are 8 options for the third point, yielding 12 * 8 = 96 potential triangles. However, isosceles triangles, formed when the third point coincides with one of the initial points creating the 45-degree angle, have been counted twice. Subtracting these 12 duplicate isosceles triangles leaves us with a total of 84 distinct triangles.

Keywords

circle

triangles

45-degree angle

isosceles

geometry