in the following diagram, point $g$ represents the centroid of the triangle. determine the length of $\overline{cg}$ given that $\overline{dc} = 33$.

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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Centroid Theorem" ], "new_concepts": [], "current_concepts": [ "Centroid Theorem", "Median of a Triangle" ] } ## Identify the median and centroid relationship Using the *Centroid Theorem* knowledge point $$ \begin{aligned} &\text{Segment } \overline{DC} \text{ is a median of } \triangle ABC \text{ with centroid } G.\ &CG = \frac{2}{3}DC \end{aligned} $$ ## Calculate the length of CG Using the *Centroid Theorem* knowledge point $$ \begin{aligned} &DC = 33\ &CG = \frac{2}{3} \times 33 = 22 \end{aligned} $$ $CG = 22$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Geometry", "Centroid Theorem" ] }

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Identify the median and centroid relationship

Calculate the length of CG

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