tangent lines

what is the perimeter of this red polygon?
? cm

Question

tangent lines

what is the perimeter of this red 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 the properties of the circumscribed polygon Using the *Tangent Segments Theorem* and *Circumscribed Polygon* knowledge points $$ \begin{aligned} &\text{Let the vertices of the quadrilateral be } A, B, C, D \text{ in order.}\ &\text{Let the points of tangency on sides } AB, BC, CD, DA \text{ divide each side into two segments.}\ &\text{Tangent segments from a common external point to a circle are equal in length.}\ &\text{The given segment lengths from the vertices to the tangency points are: } 3\text{ cm}, 2\text{ cm}, 4\text{ cm}, 4\text{ cm.} \end{aligned} $$ ## Calculate the sum of all tangent segments Using the *Tangent Segments Theorem* and *Circumscribed Polygon* knowledge points $$ \begin{aligned} P &= 2 \times (3\text{ cm} + 2\text{ cm} + 4\text{ cm} + 4\text{ cm})\ P &= 2 \times 13\text{ cm}\ P &= 26\text{ cm} \end{aligned} $$ What is the perimeter of this red polygon? 26 $cm$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Tangent Segments Theorem" ] }

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Question

Explanation:

Identify the properties of the circumscribed polygon

Calculate the sum of all tangent segments

Answer: