line segment ts is tangent to circle o at point n. if the measure of $\angle qnt$ is $74^\circ$, what is the measure of $\widehat{qpn}$?

$37^\circ$
$74^\circ$
$148^\circ$
$212^\circ$

Question

line segment ts is tangent to circle o at point n. if the measure of $\angle qnt$ is $74^\circ$, what is the measure of $\widehat{qpn}$?

$37^\circ$
$74^\circ$
$148^\circ$
$212^\circ$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Circle Geometry", "Tangent Line to Circle" ], "new_concepts": [ "Tangent-Secant Theorem", "Tangent-Chord Theorem", "Arc Measure" ], "current_concepts": [ "Circle Geometry", "Tangent Line to Circle", "Tangent-Chord Theorem", "Arc Measure" ] } ## Relate the tangent-chord angle to the intercepted arc $$ m\widehat{QN} = 2 \cdot m\angle QNT = 2 \cdot 74^\circ = 148^\circ $$ ## Determine the measure of the major arc $$ m\widehat{QPN} = 360^\circ - m\widehat{QN} = 360^\circ - 148^\circ = 212^\circ $$

37°

74°

148°

212°

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Circle Geometry" ] }

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QUESTION IMAGE

Question

Explanation:

Relate the tangent-chord angle to the intercepted arc

Determine the measure of the major arc

Answer: