find $x$.

$x =$

Question

find $x$.

$x =$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Tangent-Secant Theorem" ], "current_concepts": [ "Tangent-Secant Theorem" ] } ## Identify the geometric components $$ \begin{aligned} &\text{Tangent segment length: } t = x \ &\text{External secant segment length: } e = 9 \ &\text{Internal secant segment (chord) length: } c = 27 \ &\text{Total secant segment length: } s = e + c = 9 + 27 = 36 \end{aligned} $$ ## Apply the Tangent-Secant Theorem $$ \begin{aligned} &t^2 = e \cdot s \ &x^2 = 9 \cdot 36 \ &x^2 = 324 \end{aligned} $$ ## Solve for x $$ \begin{aligned} &x = \sqrt{324} \ &x = 18 \end{aligned} $$ Find $x$. $x =$ 18 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Tangent-Secant Theorem" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the geometric components

Apply the Tangent-Secant Theorem

Solve for x

Answer: