in circle a, $\angle bae \cong \angle dae$

what is the length of $\overline{be}$?

14 units
17 units
27 units
34 units

Question

in circle a, $\angle bae \cong \angle dae$

what is the length of $\overline{be}$?

14 units
17 units
27 units
34 units

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Congruent Arcs", "Circle Geometry" ], "new_concepts": [ "Congruent Chords Theorem" ], "current_concepts": [ "Congruent Arcs", "Circle Geometry", "Congruent Chords Theorem" ] } ## Equate the chord lengths $$ \begin{aligned} \angle BAE &\cong \angle DAE \implies \widehat{BE} \cong \widehat{DE} \implies BE = DE \ 3x - 24 &= x + 10 \end{aligned} $$ ## Solve for x $$ \begin{aligned} 2x &= 34 \ x &= 17 \end{aligned} $$ ## Calculate the length of BE $$ \begin{aligned} BE &= 3(17) - 24 \ BE &= 51 - 24 \ BE &= 27 \end{aligned} $$

14 units

17 units

27 units

34 units

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Circle Geometry" ] }

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QUESTION IMAGE

Question

Explanation:

Equate the chord lengths

Solve for x

Calculate the length of BE

Answer: