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Geometry & Trig Traps

Circles, vectors, and proportions. Solve with vision, not just variables.

Difficulty: ★★★★☆

The Hidden Circle

Radius of the circle: \(x^2 + y^2 + 6x - 8y = 0\)?

🚩 The Trap

Getting lost in "completing the square." One sign error and you pick the wrong choice.

✅ The Practix Shortcut

Halve and square. Take the coefficients of x and y, halve them, square them, and add them.

3² + 4² = 25 \(\rightarrow\) r = 5

Answer: 5.

Difficulty: ★★★★★

The Pizza Slice Puzzle

Radius 10, Sector Area \(20\pi\). Central angle in radians?

🚩 The Trap

Mixing up the area vs arc length formulas. It's a classic Module 2 distractor.

✅ The Practix Shortcut

Use the Master Proportion: Area / Total Area = Angle / \(2\pi\).

\(\frac{1}{5} = \frac{\theta}{2\pi} \rightarrow \theta = \frac{2\pi}{5}\)

Answer: 2π/5.