Grades 11-12 Video Solutions 2025-2025_11-12

Video Transcription

Video Summary

The problem involves finding the number of triangles that can be formed with vertices at any three of the eight points (A, B, C, D, E, F, G, H) on a semicircle with diameter AD. The solution involves calculating the total number of triangles as 8 choose 3, which is 56. Then, subtract the invalid cases where all three points are collinear, which occurs only when all three points are on the diameter (A, B, C, D). This provides 4 choose 3 invalid triangles, totalling 4. By subtracting these from the total, we get 52 valid triangles, corresponding to answer choice D.

Keywords

triangles

semicircle

vertices

combinatorics

collinear