ab is tangent to the circle.
ab is tangent to the circle.
ab is tangent to the circle.

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Accepted Answer

{ "quality": "clear", "question_count": 3, "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" ] } ## Verify the first triangle $$ \begin{aligned} &a = 10.6,\quad b = 14.4\ &a^2 + b^2 = 10.6^2 + 14.4^2 = 112.36 + 207.36 = 319.72\ &c = 7.4 + 10.6 = 18\ &c^2 = 18^2 = 324\ &a^2 + b^2 eq c^2 \implies \text{is not} \end{aligned} $$ ## Verify the second triangle $$ \begin{aligned} &a = 12,\quad b = 12.6\ &a^2 + b^2 = 12^2 + 12.6^2 = 144 + 158.76 = 302.76\ &c = 5.4 + 12 = 17.4\ &c^2 = 17.4^2 = 302.76\ &a^2 + b^2 = c^2 \implies \text{is} \end{aligned} $$ ## Verify the third triangle $$ \begin{aligned} &a = 8,\quad b = 13\ &a^2 + b^2 = 8^2 + 13^2 = 64 + 169 = 233\ &c = 20\ &c^2 = 20^2 = 400\ &a^2 + b^2 eq c^2 \implies \text{is not} \end{aligned} $$ ## Question 1 AB is not tangent to the circle. ## Question 2 AB is tangent to the circle. ## Question 3 AB is not tangent to the circle. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Tangent-Radius Angle" ] }

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Explanation:

Verify the first triangle

Verify the second triangle

Verify the third triangle

Answer:

Question 1

Question 2

Question 3