what is the value of $x$?

$\bigcirc$ 2
$\bigcirc$ 3
$\bigcirc$ 6
$\bigcirc$ 7

Question

what is the value of $x$?

$\bigcirc$ 2
$\bigcirc$ 3
$\bigcirc$ 6
$\bigcirc$ 7

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Secant-Secant Theorem" ], "new_concepts": [], "current_concepts": [ "Secant-Secant Theorem", "Circle Geometry" ] } ## Identify the given segment lengths $$ \begin{aligned} &AE = AB + BE = 11 + (x + 1) = x + 12\ &BE = x + 1\ &DE = DC + CE = 1 + (x + 4) = x + 5\ &CE = x + 4 \end{aligned} $$ ## Apply the Secant-Secant Theorem $$ \begin{aligned} &BE \cdot AE = CE \cdot DE\ &(x + 1)(x + 12) = (x + 4)(x + 5) \end{aligned} $$ ## Solve for x $$ \begin{aligned} &x^2 + 13x + 12 = x^2 + 9x + 20\ &13x + 12 = 9x + 20\ &4x = 8\ &x = 2 \end{aligned} $$

(A) 2

(B) 3

(C) 6

(D) 7

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Secant-Secant Theorem" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Identify the given segment lengths

Apply the Secant-Secant Theorem

Solve for x

Answer: