unit exam - circles

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

$eb = ?$

Question

unit exam - circles

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" ], "new_concepts": [], "current_concepts": [ "Equidistant Chords Theorem", "Perpendicular Bisector of Chord" ] } ## Identify congruent chords using the equidistant chords theorem $$ \begin{aligned} &d(O, AB) = 5 \ &d(O, CD) = 5 \ &d(O, AB) = d(O, CD) \implies AB = CD = 18 \end{aligned} $$ ## Apply the perpendicular bisector theorem to find the segment length $$ \begin{aligned} &OE \perp AB \implies EB = \frac{1}{2} AB \ &EB = \frac{1}{2} (18) = 9 \end{aligned} $$ Find the length of $\overline{EB}$. $EB =$ 9 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Equidistant Chords Theorem" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Identify congruent chords using the equidistant chords theorem

Apply the perpendicular bisector theorem to find the segment length

Answer: