must complete all four challenges for full credit
line $ih$ is tangent to circle $n$.
what is $m\angle nih$ in radians?

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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": [ "Degree to Radian Conversion" ], "new_concepts": [ "Tangent Line to Circle", "Isosceles Triangle Properties" ], "current_concepts": [ "Degree to Radian Conversion", "Tangent Line to Circle", "Isosceles Triangle Properties" ] } ## Identify geometric properties of the triangle $$ \begin{aligned} &\text{Line } IH \text{ is tangent to circle } N \text{ at point } H \implies \angle NHI = 90^\circ\ &NH = IH \implies \triangle NHI \text{ is an isosceles right triangle} \end{aligned} $$ ## Calculate the target angle in degrees $$ \begin{aligned} &m\angle NIH = \frac{180^\circ - 90^\circ}{2} = 45^\circ \end{aligned} $$ ## Convert the angle measure to radians $$ \begin{aligned} &m\angle NIH = 45^\circ \times \frac{\pi}{180^\circ} = \frac{\pi}{4} \end{aligned} $$ Line $IH$ is tangent to circle $N$. What is $m\angle NIH$ in radians? $\frac{\pi}{4}$ radians { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Tangent Line to Circle" ] }

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Question

Explanation:

Identify geometric properties of the triangle

Calculate the target angle in degrees

Convert the angle measure to radians

Answer: