question 10 of 10

fill in the blank. given $\odot e$ below, you can conclude that $\overline{cd}$ is congruent to ______.

a. $\odot e$
b. $\overline{eg}$
c. $\overline{fb}$
d. $\overline{ab}$

Question

question 10 of 10

fill in the blank. given $\odot e$ below, you can conclude that $\overline{cd}$ is congruent to ______.

a. $\odot e$
b. $\overline{eg}$
c. $\overline{fb}$
d. $\overline{ab}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Equidistant Chords Theorem" ], "new_concepts": [], "current_concepts": [ "Equidistant Chords Theorem", "Chord Definition", "Circle Theorems" ] } ## Identify given geometric properties $$ \begin{aligned} &EF \perp AB, \quad EG \perp CD \ &EF = 3.4, \quad EG = 3.4 \ &EF = EG \end{aligned} $$ ## Apply the Equidistant Chords Theorem $$ \begin{aligned} &d(E, AB) = d(E, CD) \implies AB \cong CD \end{aligned} $$ ## Match with the given options $$ \overline{CD} \cong \overline{AB} $$

A. $\odot E$

B. $\overline{EG}$

C. $\overline{FB}$

D. $\overline{AB}$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Equidistant Chords Theorem" ] }

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QUESTION IMAGE

Question

Explanation:

Identify given geometric properties

Apply the Equidistant Chords Theorem

Match with the given options

Answer: