Chapter 1: Introduction to the Geometry Problem

Approximately ten days ago, I tackled a geometry question from the Oxford University MAT. Initially, I devised a personal method by calculating the individual radii of the circles involved. However, I soon discovered a much swifter route to the solution.

Here’s the original question for your reference!

Here's a significant clue: consider connecting one side to the opposite side.

I encourage you to pause here, take out some paper and a pen, and give it a try. When you feel prepared, continue reading for the answer!

Section 1.1: The Elegant Solution

The radius of the larger circle is denoted as r1, while the radius of the smaller circle is r2.

By establishing a connection between the square's sides, we can derive a formula for the side length based on r1 and r2.

This line consists of a blue segment on the left, a green segment in the center, and an orange segment on the right.

Using the Pythagorean Theorem, we can determine the expressions for the green segments.

This leads us to the following equation.

The objective of this problem is to calculate the value of r1 + r2. This should be straightforward for everyone!

What an elegant solution...

Photo credit: Marc Schulte on Unsplash

And that concludes our answer.

How remarkable!

What were your thoughts during this process? I would love to hear your insights in the comments below!

Chapter 2: Additional Resources

In this video titled "Worked Solution for Oxford University MAT 2021 (Dodecagon Question, 1A)," you will find a comprehensive breakdown of the geometry problem and its solutions.

This second video, "MAT livestream 2024 - Geometry," provides further insights into various geometry problems, enhancing your understanding and problem-solving skills.

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Happy Solving, Bella 😊