Mathematics is full of intriguing puzzles that challenge our problem-solving skills. Today, let’s tackle an interesting problem involving a circle enclosing nested squares.
Problem Statement
In the image below, we have a circle enclosing three squares arranged in a staircase pattern. The side lengths of the squares are:
- 1 cm (smallest square)
- 2 cm (middle square)
- 3 cm (largest square)
The task is to determine the radius of the circle that encloses these squares.
Steps to Solve
1. Understand the Structure
- The squares are arranged in a stepwise manner, forming a diagonal structure inside the circle.
- The rightmost point of the largest square touches the boundary of the circle.
2. Break Down the Problem
- Identify key geometric properties, such as the relationship between the squares and the circle.
- Consider using coordinate geometry, the Pythagorean theorem, or other mathematical techniques to approach the solution.
3. Apply the Right Formula
- Explore different ways to express the circle’s radius using the given square sizes.
- Use logical steps to derive the correct formula without assumptions.
Try It Yourself!
Give this problem a try and leave your solution in the comments! Stay tuned for the full step-by-step explanation in the next post. 🚀
