$ab$ is / is not tangent to the circle.

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Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Tangent-Radius Angle", "Pythagorean Theorem Application" ], "new_concepts": [], "current_concepts": [ "Tangent-Radius Angle", "Pythagorean Theorem Application", "Converse of Pythagorean Theorem" ] } ## Identify the side lengths of the triangle $$ \begin{aligned} &\text{Let } O \text{ be the center of the circle.}\ &AB = 15\ &OB = 8\ &AO = 17 \end{aligned} $$ ## Apply the Converse of the Pythagorean Theorem $$ \begin{aligned} &AB^2 + OB^2 = 15^2 + 8^2 = 225 + 64 = 289\ &AO^2 = 17^2 = 289\ &AB^2 + OB^2 = AO^2 \end{aligned} $$ ## Determine the tangent relationship $$ \begin{aligned} &\angle ABO = 90^\circ\ &AB \perp OB \text{ at point } B \text{ on the circle}\ &\overline{AB} \text{ is tangent to the circle} \end{aligned} $$ $\overline{AB}$ is tangent to the circle. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Tangent-Radius Angle" ] }

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Question

Explanation:

Identify the side lengths of the triangle

Apply the Converse of the Pythagorean Theorem

Determine the tangent relationship

Answer: