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Centroid Divides Median in the Ratio 2:1

In Δ ABC, the...

Question

In $Δ$ ABC, the medians BE and CF intersect at G. AD is a line meeting BC at D. If GD is 1.5 cm, then find the value of AD.

2.5 cm

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3 cm

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4 cm

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4.5 cm

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Solution

The correct option is D 4.5 cm
$A G : G D = 2 : 1 \Rightarrow G D : A D = 1 : 3$
$\Rightarrow A D : G D = 3 : 1$
$\frac{A D}{G D} = \frac{3}{1}$
$\Rightarrow \frac{A D}{1.5} = 3$
$\Rightarrow A D = 4.5$ cm.

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