Chapter 1: Introduction to the Puzzle

Greetings, everyone! As we embrace this lovely Sunday, let’s take a moment to unwind with a delightful math puzzle. This particular challenge revolves around three vibrant circles nestled within a larger circle.

To give you a nudge in the right direction: remember, a complete circle encompasses 360 degrees, and if we split that by three, what do we get?

I suggest taking a brief pause to grab some pen and paper before you tackle this puzzle. Once you're ready, continue reading to uncover the solution!

Section 1.1: Analyzing the Colorful Circles

Focus your attention on the three colorful circles; we will analyze one of them closely.

In this scenario, O represents the center of the outer circle, while C denotes the center of one of the smaller circles. The line segments OA and OB act as tangents to the smaller circle, as illustrated.

Subsection 1.1.1: Understanding the Angles

The three highlighted angles are equal and collectively total 360 degrees, indicating that each angle measures 120 degrees. When we bisect one of these angles, we arrive at 120/2 = 60 degrees. Consequently, triangle AOC forms a 30–60–90 degree right triangle, where AC represents the radius of the smaller circle, measuring 1.

Utilizing trigonometric principles, we calculate:

Section 1.2: Calculating the Radius of the Larger Circle

The radius of the larger circle can be expressed as OD = OC + CD.

By summing these lengths, we can determine the final answer.

Isn't that fascinating?

What were your thoughts while solving this puzzle? I invite you to share your insights in the comments below—I’m eager to hear from you!

Chapter 2: Expand Your Math Skills

To further enhance your mathematical abilities, check out the following video that challenges your intellect:

The first video titled "Are You Smart Enough For College? (100 Questions Quiz)" offers an engaging series of questions that can test your academic readiness.

Additionally, explore the second video "Are You Smart Enough to Ace this Guitar Test? (Eleven Questions)" to put your skills to the test in a fun and musical way.

Feel free to save and share this list of the best math puzzles on Medium with your friends!

Math Puzzles

Discover an array of intriguing math puzzles covering Algebra, Geometry, Calculus, Number Theory, and more.

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With gratitude, Bella