The "Impossible" Tangent Square Problem

Can You Solve This Viral Geometry Challenge? | Circle & Square Math Puzzle
Are you ready for a math challenge for students that will push your logic and problem-solving skills to the limit? Welcome back to Trick = Treat, where we provide clever math and clean solutions.

In today’s video, we tackle a classic circle and square problem that is perfect for anyone currently in Math Olympiad training or working on AMC 10 preparation and AMC 12 math. This figure represents a beautiful example of mathematical symmetry, but it requires more than just a quick glance to solve.

What you’ll learn in this video:

How to identify and utilize symmetry in hard geometry questions.
A step-by-step breakdown of applying the Pythagorean Theorem practice to complex shapes.
The intersection of algebra and geometry: solving quadratic equations to find a geometric area.
Competitive math techniques used in the Math Olympiad geometry circuit and AIME math problems.
Whether you are studying for SAT Math geometry, preparing for a geometry competition prep session, or just love math puzzles with solutions, this video is for you. We bridge the gap between advanced high school math and professional competition-level thinking.
Can you find the area of the square with only one clue? Watch the full video to see the "trick" that makes the "treat" of a solution so satisfying!
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Chapters:
0:00 The "Impossible" Problem
1:05 Setting up the Variables (Radius R, Side A)
2:40 Finding the Right Triangle
3:45 Pythagorean Theorem Setup
4:54 The Quadratic Solution
5:47 The Secret "Zero Area" Solution
#MathOlympiad #Geometry #MathPuzzle #AMC10 #AMC12 #SATMath #HighSchoolMath #STEM #PythagoreanTheorem #Algebra #ProblemSolving