Grades 11-12 Video Solutions 2014-11&12 Video Solutions 2014 problem24

11&12 Video Solutions 2014 problem24

Video Transcription

Video Summary

The problem involves fitting a square between a horizontal line and two touching circles, each with a radius of 1. The objective is to find the side length of the square. By constructing a rectangle and using geometry and algebra, the problem is solved using the equations derived from the circle and square dimensions. Solving the equations yields two potential solutions for the side length, x. However, the valid solution respecting the dimensions (since x must be less than the diameter of the circle) is \( x = \frac{2}{5} \). Thus, the square's side length is \( \frac{2}{5} \).

Keywords

geometry

square

circle

algebra

solution