chords and arcs

find the length of $\overline{eb}$.

$eb = ?$

Question

chords and arcs

find the length of $\overline{eb}$.

$eb = ?$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Equidistant Chords Theorem", "Perpendicular Bisector of Chord", "Congruent Chords Theorem" ], "new_concepts": [], "current_concepts": [ "Equidistant Chords Theorem", "Perpendicular Bisector of Chord", "Congruent Chords Theorem" ] } ## Identify congruent chords using distance from the center $$ \begin{aligned} &d(\text{Center}, AB) = 5 \ &d(\text{Center}, CD) = 5 \ &\text{Since distances are equal, } AB = CD = 18 \end{aligned} $$ ## Apply perpendicular bisector property to find EB $$ \begin{aligned} &\text{Segment from center is perpendicular to chord } AB \text{ at } E \ &EB = \frac{1}{2} \cdot AB \ &EB = \frac{1}{2} \cdot 18 = 9 \end{aligned} $$ Find the length of $\overline{EB}$. $EB =$ 9 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Congruent Chords Theorem" ] }

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Question

Explanation:

Identify congruent chords using distance from the center

Apply perpendicular bisector property to find EB

Answer: