SAT Math Practice Question #747 (Hard (800)) | Test Citadel
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SAT Math Difficulty: Hard (800)

Digital SAT Math Practice Question #747

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 passes through the origin \( (0,0) \) and has its center at \( (h, k) \). The circle intersects the positive x-axis at \( (a, 0) \) and the positive y-axis at \( (0, b) \), where \( a > 0 \) and \( b > 0 \). If the area of the circle is \( 169\pi \) and \( a = 10 \), what is the value of \( b \)?
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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)

Desmos Tactical Shortcut: Plot the left-hand side and right-hand side as separate equations (e.g. \( y_1 = f(x) \) and \( y_2 = g(x) \)). Click the intersection points directly to read exact coordinates.

Masterclass Solution & Distractor Trap Analysis

This is a stunning geometry problem that rewards students who recognize a classic circle theorem: Thales's Theorem. Let's visualize the scenario. The circle passes through three key points: \( (0,0) \), \( (10,0) \), and \( (0,b) \). Becaus...

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

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