what is the length of the indicated segment?

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{ "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" ] } ## Identify the given values and theorem $$ \begin{aligned} &\text{Tangent segment length } (t) = x \ &\text{External secant segment length } (e) = 8 \ &\text{Internal secant segment (diameter) length } (d) = 32.5 \ &\text{Total secant segment length } (s) = e + d = 8 + 32.5 = 40.5 \ &\text{Theorem: } t^2 = e \cdot s \end{aligned} $$ ## Solve for x $$ \begin{aligned} &x^2 = 8 \cdot 40.5 \ &x^2 = 324 \ &x = \sqrt{324} = 18 \end{aligned} $$ What is the length of the indicated segment? 18 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Tangent-Secant Theorem" ] }

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Identify the given values and theorem

Solve for x

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