Question : G and AD are respectively the centroid and median of the triangle $\triangle$ABC. The ratio AG : AD is equal to:
Option 1: 3 : 2
Option 2: 2 : 3
Option 3: 2 : 1
Option 4: 1 : 2
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Correct Answer: 2 : 3
Solution : The point of intersection of the medians of a triangle is called the centroid. It divides each median in the ratio 2 : 1. So, $\frac{AG}{GD}=\frac{2}{1}$ Let AG = 2 units, GD = 1 unit $\therefore$ AD = AG + GD = 2 + 1 = 3 units Now, $\frac{AG}{AD}=\frac{2}{3}$ $\therefore$ AG : AD = 2 : 3 Hence, the correct answer is 2 : 3.
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