SAT Math Practice Question #717 (Hard (800)) | Test Citadel
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SAT Math Difficulty: Hard (800)

Digital SAT Math Practice Question #717

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

In the \( xy \)-plane, a circle with center \( O \) at the origin has a radius of \( 8 \). The points \( A \) and \( B \) lie on the circle such that the measure of angle \( AOB \) is \( \frac{3\pi}{4} \) radians. What is the straight-line distance between points \( A \) and \( B \)?
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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

We are looking for the length of a chord (the straight line \( AB \)) in a circle given the radius and the central angle. We have a triangle \( AOB \) where \( O \) is the center of the circle. The lengths of sides \( OA \) and \( OB \) are...

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

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