SAT Math Practice Question #258 (Hard (710)) | Test Citadel
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SAT Math Difficulty: Hard (710)

Digital SAT Math Practice Question #258

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

A circle in the \(xy\)-plane has its center at the origin. The total area of the circle is \( 144\pi \). A sector of the circle is bounded by radii \( OA \) and \( OB \). If the arc length of the sector is \( 10\pi \), what is the measure of angle \( AOB \), in radians?
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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

Geometry and trigonometry meet here in a classic SAT circle problem! Let's take it step-by-step to uncover the mystery of angle \( AOB \). Step 1: Find the radius. We know the area of the circle is \( 144\pi \). The formula for the area of ...

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

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