The given triangle has Centroid at O.

If PC = 54 cm, Find the length of OC.

42 cm

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36 cm

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24 cm

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18 cm

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Solution

The correct option is B
36 cm

PC is a Median and O is the centroid.

Centroid Divides Median in the Ratio 2 : 1.

OC : OP = 2 : 1

OC = 2x and OP = x

PC = OC + OP = 2x + x = 3x

3x = 54

$\Rightarrow$ x = 18 cm

$∴$ Length of OC = 2x = 2 $\times$ 18 = 36 cm

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