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Can You Solve This Geometry Riddle? (95% Fail)

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Can You Solve This Geometry Riddle? (95% Fail)

This math riddle presents a fun geometry problem that challenges many. It involves a small square touching four circles inscribed within a larger square. The goal is to find the area of the smaller square. This riddle is a great way to test your understanding of geometric concepts and problem-solving skills.

The Riddle

Imagine a larger square with four circles inscribed inside it, each touching the sides of the square and the other circles. Now, a smaller square is drawn inside, touching all four circles. If the side of the larger square is 2 units, what is the area of the smaller square?

Solution

Here's how to solve this intriguing geometry riddle:

  1. Connect the Centers: Draw lines connecting the centers of the four circles. This will form a smaller square at the center, with sides equal to the diameter of the circles.
  2. Radius and Diameter: The diameter of each circle is equal to the side of the larger square, which is 2 units. Therefore, the radius of each circle is 1 unit.
  3. Diagonal of Smaller Square: The diagonal of the smaller square (formed by connecting the centers) is equal to the diameter of two circles, which is 2 + 2 = 4 units.
  4. Pythagorean Theorem: We can use the Pythagorean theorem to find the side of the smaller square. Let 's' be the side of the smaller square. The diagonal of the smaller square is the hypotenuse of a right triangle formed by two sides of the smaller square. So, s2 + s2 = 42.
  5. Solve for 's': Simplifying the equation, we get 2s2 = 16. Solving for 's', we get s2 = 8, and s = √8 = 2√2.
  6. Area of Smaller Square: The area of the smaller square is s2 = (2√2)2 = 8 square units.

Key Takeaways

  • Visualizing Shapes: This riddle emphasizes the importance of visualizing geometric shapes and their relationships.
  • Using Key Concepts: Understanding concepts like radius, diameter, and the Pythagorean theorem is crucial for solving this problem.
  • Problem-Solving Skills: This riddle demonstrates how to break down a complex problem into smaller, manageable steps.

Did you manage to solve this geometry riddle? If not, don't worry! It's a challenging one. Practice more geometry problems, and you'll be solving these riddles in no time.

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