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", "Secant-Secant Theorem" ] } ## Identify the geometric theorem $$ \text{External Segment} \times \text{Entire Secant} = \text{External Segment} \times \text{Entire Secant} $$ ## Set up the equation $$ 15 \times (15 + 27) = x \times 45 $$ ## Solve for x $$ \begin{aligned} 15 \times 42 &= 45x \ 630 &= 45x \ x &= 14 \end{aligned} $$ What is the length of the indicated segment? 14 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Tangent-Secant Theorem" ] }

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Explanation:

Identify the geometric theorem

Set up the equation

Solve for x

Answer: