find the length of the indicated segment. assume lines which appear to be tangent are tangent. write your answer as a decimal to the nearest tenth.

the length of the segment is

Question

find the length of the indicated segment. assume lines which appear to be tangent are tangent. write your answer as a decimal to the nearest tenth.

the length of the segment is

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Tangent-Secant Theorem" ], "new_concepts": [], "current_concepts": [ "Tangent-Secant Theorem", "Circle Geometry" ] } ## Apply the Tangent-Secant Theorem $$ \begin{aligned} &\text{Tangent segment } (t) = 9.9 \ &\text{External secant segment } (e) = x - 6.6 \ &\text{Entire secant segment } (s) = x \ &t^2 = e \cdot s \ &9.9^2 = (x - 6.6) \cdot x \end{aligned} $$ ## Solve the quadratic equation for x $$ \begin{aligned} &98.01 = x^2 - 6.6x \ &x^2 - 6.6x - 98.01 = 0 \ &x = \frac{6.6 \pm \sqrt{(-6.6)^2 - 4(1)(-98.01)}}{2} \ &x = \frac{6.6 \pm \sqrt{43.56 + 392.04}}{2} \ &x = \frac{6.6 \pm \sqrt{435.6}}{2} \ &x \approx \frac{6.6 + 20.871}{2} \approx 13.735 \end{aligned} $$ ## Round to the nearest tenth $$ x \approx 13.7 $$ Find the length of the indicated segment. Assume lines which appear to be tangent are tangent. Write your answer as a decimal to the nearest tenth. The length of the segment is 13.7 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Tangent-Secant Theorem" ] }

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QUESTION IMAGE

Question

Explanation:

Apply the Tangent-Secant Theorem

Solve the quadratic equation for x

Round to the nearest tenth

Answer: