question 9 of 10

true or false? a circle could be circumscribed about the quadrilateral below.

a. true
b. false

Question

question 9 of 10

true or false? a circle could be circumscribed about the quadrilateral below.

a. true
b. false

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Inscribed Quadrilateral Theorem", "Circumscribed Circle" ], "new_concepts": [], "current_concepts": [ "Inscribed Quadrilateral Theorem", "Circumscribed Circle", "Rectangle Definition" ] } ## Identify the properties of the given quadrilateral $$ \angle A = 90^\circ, \quad \angle B = 90^\circ, \quad \angle C = 90^\circ, \quad \angle D = 90^\circ $$ ## Apply the Inscribed Quadrilateral Theorem $$ \begin{aligned} &\angle A + \angle C = 90^\circ + 90^\circ = 180^\circ\ &\angle B + \angle D = 90^\circ + 90^\circ = 180^\circ \end{aligned} $$ ## Determine if a circle can be circumscribed $$ \text{Opposite angles are supplementary} \implies \text{The quadrilateral is cyclic (can be circumscribed by a circle).} $$

A. True

B. False

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Inscribed Quadrilateral Theorem" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the properties of the given quadrilateral

Apply the Inscribed Quadrilateral Theorem

Determine if a circle can be circumscribed

Answer: