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Question

The length of tangent from point (5, 4) to circle x² + y² = 9 is

RankGuru · Accepted Answer

1. **Formula**: The length of a tangent $L$ from an external point $(x_1, y_1)$ to circle $x^2 + y^2 - r^2 = 0$ is $L = \sqrt{x_1^2 + y_1^2 - r^2}$.
2. **Identify Data**: Point is $(5, 4)$, Circle is $x^2 + y^2 - 9 = 0$ ($r^2 = 9$).
3. **Calculate Power of Point**:
   - $S_1 = 5^2 + 4^2 - 9 = 25 + 16 - 9 = 32$.
4. **Extract Length**:
   - $L = \sqrt{32} = 4\sqrt{2}$.

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