which equation shows the correct application of the secant-tangent segment theorem to the figure?

$12(a + 12) = 10^2$
$10 + 12 = a^2$
$10(a + 10) = 12^2$
$10(12) = a^2$

Question

which equation shows the correct application of the secant-tangent segment theorem to the figure?

$12(a + 12) = 10^2$
$10 + 12 = a^2$
$10(a + 10) = 12^2$
$10(12) = a^2$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Tangent-Secant Theorem" ], "current_concepts": [ "Tangent-Secant Theorem", "Circle Geometry" ] } ## Identify the given segments $$ \begin{aligned} &\text{External secant segment} = 10\ &\text{Internal secant segment (chord)} = a\ &\text{Entire secant segment} = 10 + a\ &\text{Tangent segment} = 12 \end{aligned} $$ ## Apply the tangent-secant theorem $$ \begin{aligned} &\text{External Secant} \times \text{Entire Secant} = (\text{Tangent})^2\ &10(a + 10) = 12^2 \end{aligned} $$

$12(a + 12) = 10^2$

$10 + 12 = a^2$

$10(a + 10) = 12^2$

$10(12) = a^2$

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

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Identify the given segments

Apply the tangent-secant theorem

Answer: