ACT Math Practice Question #817 (Hard (36)) | Test Citadel
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ACT Math Difficulty: Hard (36)

Digital ACT Math Practice Question #817

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 \( (3, -2) \) and is tangent to the line \( 4x - 3y = 25 \). What is the area of the circle?
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Socratic AI Engine Step-by-Step Derivation
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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 radius of a circle tangent to a line is the perpendicular distance from the center of the circle to the line. The center of the circle is given as \( (x_0, y_0) = (3, -2) \). The equation of the tangent line is \( 4x - 3y = 25 \). To us...

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

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