line segment xy is tangent to circle z at point u.
if the measure of $\widehat{uv}$ is $84^\circ$, what is the measure of $\angle yuv$?

$42^\circ$
$84^\circ$
$96^\circ$
$168^\circ$

Question

line segment xy is tangent to circle z at point u.
if the measure of $\widehat{uv}$ is $84^\circ$, what is the measure of $\angle yuv$?

$42^\circ$
$84^\circ$
$96^\circ$
$168^\circ$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Tangent-Chord Theorem" ], "new_concepts": [], "current_concepts": [ "Tangent-Chord Theorem", "Circle Geometry" ] } ## Identify the given geometric properties $$ \begin{aligned} &\text{Line } XY \text{ is tangent to circle } Z \text{ at point } U.\ &V \text{ is a point on circle } Z.\ &m\widehat{UV} = 84^\circ \end{aligned} $$ ## Apply the Tangent-Chord Theorem $$ \begin{aligned} &m\angle YUV = \frac{1}{2} \cdot m\widehat{UV} \end{aligned} $$ ## Calculate the angle measure $$ \begin{aligned} &m\angle YUV = \frac{1}{2} \cdot 84^\circ = 42^\circ \end{aligned} $$

(A) $42^\circ$

(B) $84^\circ$

(C) $96^\circ$

(D) $168^\circ$

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

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QUESTION IMAGE

Question

Explanation:

Identify the given geometric properties

Apply the Tangent-Chord Theorem

Calculate the angle measure

Answer: