tangent lines

what is the perimeter of this polygon?

? cm

Question

tangent lines

what is the perimeter of this polygon?

?  cm

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Tangent Segments Theorem", "Circumscribed Polygon" ], "new_concepts": [], "current_concepts": [ "Tangent Segments Theorem", "Circumscribed Polygon" ] } ## Identify tangent segments from each vertex Using the *Tangent Segments Theorem* and *Circumscribed Polygon* knowledge points $$ \begin{aligned} &\text{Let the points of tangency on } AB, BC, \text{ and } AC \text{ be } P, Q, \text{ and } R \text{ respectively.}\ &AP = AR = 3\text{ cm}\ &BP = BQ = 3\text{ cm}\ &CR = CQ = 9\text{ cm} \end{aligned} $$ ## Calculate the side lengths of the triangle Using the *Circumscribed Polygon* knowledge point $$ \begin{aligned} &AB = AP + BP = 3 + 3 = 6\text{ cm}\ &BC = BQ + CQ = 3 + 9 = 12\text{ cm}\ &AC = AR + CR = 3 + 9 = 12\text{ cm} \end{aligned} $$ ## Calculate the perimeter of the polygon Using the *Circumscribed Polygon* knowledge point $$ \begin{aligned} &\text{Perimeter} = AB + BC + AC\ &\text{Perimeter} = 6 + 12 + 12 = 30\text{ cm} \end{aligned} $$ What is the perimeter of this polygon? 30 cm { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Tangent Segments Theorem" ] }

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QUESTION IMAGE

Question

Explanation:

Identify tangent segments from each vertex

Calculate the side lengths of the triangle

Calculate the perimeter of the polygon

Answer: