Tangents to a circle from an external point — A/L Combined Mathematics

How do I practise Tangents to a circle from an external point?

1 question with a worked solution

Check before you answer: Tangent Length Verification: Verifying that S₁ > 0 confirming P lies strictly outside the circle before computing tangent length L = √S₁.

1. What is the length of the tangent segment drawn from the external point P(4, 5) to the circle S ≡ x² + y² - 4x - 2y - 6 = 0?
   1. A) 3 units
   2. B) 4 units
   3. C) 9 units
   4. D) √17 units
   Check my answer

   Correct answer: A) 3 units

   The length of the tangent from a point (x₁, y₁) to the circle S = 0 is L = √(S₁₁) = √(x₁² + y₁² - 4x₁ - 2y₁ - 6). Substituting (4, 5): L = √(4² + 5² - 4(4) - 2(5) - 6) = √(41 - 32) = √9 = 3 units.

   Show worked solution

   Step 1: Formula for tangent length: L = √(x₁² + y₁² + 2gx₁ + 2fy₁ + c). Step 2: L = √(4² + 5² - 4(4) - 2(5) - 6) = √(41 - 32) = √9 = 3 units. Answer: 3 units.
   Modelled on: the A/L Combined Mathematics examination pattern

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Where does Tangents to a circle from an external point fit in the syllabus?

Year 1 · Term 3