Grades 9-10 Video Solutions 2024-2024_9-10

Video Transcription

Video Summary

To find the number of chords longer than the radius but shorter than the diameter in a circle with 20 equally spaced points, note that a chord must have a central angle greater than 60 degrees to be longer than the radius. Each adjacent pair of points forms an 18-degree angle. Therefore, central angles of 72, 90, and 108 degrees satisfy the condition. Each point connects with 12 other points via chords that meet this condition (skipping closest 3 on each side for angles less than 60). So, with 20 points, calculate \(20 \times 12 / 2\) (to account for double counting), resulting in 120 chords.

Keywords

circle

chords

geometry

central angle

equally spaced points