Multiple choice

AD is the median of the triangle ABC and O is the centroid such that AO = 12 cm. The length of OD in cm is

  1. 2

  2. 5

  3. 6

  4. 8
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C Correct answer
Explanation

The centroid O divides the median AD in the ratio 2:1. Given AO = 12 cm, we have 2x = 12, so x = 6. Since OD = x, OD = 6 cm.

AI explanation

The centroid of a triangle divides any median in the ratio of 2 to 1, with the longer part being between the vertex and the centroid. Since AD is the median and O is the centroid, the length AO is two-thirds of the total median AD, and OD is the remaining one-third. Given that AO is 12 cm, OD is simply half of AO, which is 12 divided by 2. This gives the length of OD as 6 cm. The result is 6 cm.

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