SAT Math Practice Question #608 (Hard (800)) | Test Citadel
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SAT Math Difficulty: Hard (800)

Digital SAT Math Practice Question #608

Test your problem-solving accuracy on this official-caliber item. Select an answer choice to check your reasoning instantly.

A regular hexagon is inscribed in a circle of radius 6. If a point is chosen at random from the interior of the circle, what is the probability that the point lies completely outside the boundaries of the inscribed hexagon?
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Socratic AI Engine Step-by-Step Derivation
0ms Precomputed
Tactical Insight (Hint 1)

Recall the standard circle equation: \( (x - h)^2 + (y - k)^2 = r^2 \). Complete the square if the equation is expanded.

Elimination Framework (Hint 2)

Elimination Shortcut: Check the extremes or test answer choices starting with C to binary search the correct magnitude.

Masterclass Solution & Distractor Trap Analysis

The probability that a randomly chosen point falls into a specific region is just the area of that specific region divided by the total area. Step 1: Define our regions. The 'total area' is the area of the entire circle. The 'specific regio...

Distractor Analysis: Trap choice eliminates careless test-takers who confuse roots with coordinates...

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