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

a. $\overline{oe}$
b. $\odot o$
c. $\overline{le}$
d. $\overline{tg}$

Question

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

a. $\overline{oe}$
b. $\odot o$
c. $\overline{le}$
d. $\overline{tg}$

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", "Chord Definition" ], "new_concepts": [], "current_concepts": [ "Equidistant Chords Theorem", "Chord Definition", "Circle Theorems" ] } ## Identify given geometric properties $$ \begin{aligned} &\text{Circle: } \odot O \ &\text{Chords: } \overline{TG} \text{ and } \overline{LI} \ &\text{Chord lengths: } TG = 10.4, \quad LI = 10.4 \ &\text{Distances from center } O: OH \perp TG, \quad OE \perp LI \end{aligned} $$ ## Apply the Equidistant Chords Theorem $$ \begin{aligned} &TG = LI \implies \overline{TG} \cong \overline{LI} \ &\overline{TG} \cong \overline{LI} \implies \overline{OH} \cong \overline{OE} \end{aligned} $$

A. $\overline{OE}$

B. $\odot O$

C. $\overline{LE}$

D. $\overline{TG}$

{ "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

Answer: