SAT Math Practice Question #459 (Hard (800)) | Test Citadel
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SAT Math Difficulty: Hard (800)

Digital SAT Math Practice Question #459

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

A circle with center \( O \) has a radius of \( 6 \). A secant line from a point \( P \) located outside the circle intersects the circle at points \( A \) and \( B \), such that \( A \) lies between \( P \) and \( B \). The length of segment \( PA \) is \( 4 \) and the length of chord \( AB \) is \( 5 \). A tangent line drawn from point \( P \) intersects the circle at point \( T \). What is the area of triangle \( PTO \)?
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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 geometry question is a brilliant puzzle that requires you to tie together two critical circle theorems: the Secant-Tangent Theorem (Power of a Point) and the Tangent-Radius Theorem. Step 1: Find the length of the tangent segment PT. Th...

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

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