angle d is a circumscribed angle of circle o.

what is the perimeter of kite obde?

17 units
23 units
27 units
60 units

Question

angle d is a circumscribed angle of circle o.

what is the perimeter of kite obde?

17 units
23 units
27 units
60 units

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Kite Properties", "Pythagorean Theorem", "Tangent Segments from External Point" ], "new_concepts": [], "current_concepts": [ "Kite Properties", "Pythagorean Theorem", "Tangent Segments from External Point", "Circle Geometry" ] } ## Find the radius of circle O $$ \begin{aligned} &AC = 15,\quad CB = 8\ &\angle ACB = 90^\circ \implies AB = \sqrt{AC^2 + CB^2} = \sqrt{15^2 + 8^2} = 17\ &r = OB = OE = \frac{AB}{2} = \frac{17}{2} = 8.5 \end{aligned} $$ ## Determine the tangent segment lengths $$ \begin{aligned} &BD = ED = 5 \end{aligned} $$ ## Calculate the perimeter of kite OBDE $$ \begin{aligned} &\text{Perimeter} = OB + BD + DE + EO\ &\text{Perimeter} = 8.5 + 5 + 5 + 8.5 = 27 \end{aligned} $$

17 units

23 units

27 units

60 units

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

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QUESTION IMAGE

Question

Explanation:

Find the radius of circle O

Determine the tangent segment lengths

Calculate the perimeter of kite OBDE

Answer: