question 4 of 10

which geometric object is defined as the set of all points in a plane at a given distance from a given point?

a. parabola

b. circle

c. line segment

d. line

Question

question 4 of 10

which geometric object is defined as the set of all points in a plane at a given distance from a given point?

a. parabola

b. circle

c. line segment

d. line

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "direct_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [ "Locus of Points", "Geometric Definitions" ], "new_concepts": [ "Circle Definition" ], "current_concepts": [ "Locus of Points", "Geometric Definitions", "Circle Definition" ] } ## Analyze the geometric definition The problem asks for the geometric object defined as the set of all points in a plane at a given distance from a given point. ## Identify the matching object A circle is defined as the set of all points in a plane that are at a fixed distance (the radius) from a fixed point (the center).

(A) Parabola

(B) Circle

(C) Line segment

(D) Line

{ "elements": [ { "type": "point", "params": [[0, 0]], "properties": { "name": "Center", "size": 4, "color": "#583C87", "withLabel": true } }, { "type": "circle", "params": [[0, 0], 4], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 2 } }, { "type": "point", "params": [[2.83, 2.83]], "properties": { "name": "P", "size": 4, "color": "#F2557F", "withLabel": true } }, { "type": "segment", "params": [[0, 0], [2.83, 2.83]], "properties": { "strokeColor": "#F28A55", "strokeWidth": 2, "dash": 2 } }, { "type": "text", "params": [1.2, 1.6, "r"] } ] } { "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Circle Definition" ] }

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QUESTION IMAGE

Question

Explanation:

Analyze the geometric definition

Identify the matching object

Answer: