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

a. $\odot o$
b. $\overline{el}$
c. $\overline{nl}$
d. $\overline{ao}$

Question

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

a. $\odot o$
b. $\overline{el}$
c. $\overline{nl}$
d. $\overline{ao}$

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" ] } ## Identify the given geometric properties $$ \begin{aligned} &OE \perp NL,\quad OA \perp PY\ &OE = 3,\quad OA = 3\ &OE = OA \end{aligned} $$ ## Apply the Equidistant Chords Theorem $$ \begin{aligned} &\text{Since } OE = OA \text{ and both represent perpendicular distances from center } O \text{ to chords } \overline{NL} \text{ and } \overline{PY}:\ &\overline{PY} \cong \overline{NL} \end{aligned} $$

A. $\odot O$

B. $\overline{EL}$

C. $\overline{NL}$

D. $\overline{AO}$

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

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QUESTION IMAGE

Question

Explanation:

Identify the given geometric properties

Apply the Equidistant Chords Theorem

Answer: