Multiple choice

If O, G and H are the circumcentre, the centroid and the orthocentre of a triangle ABC, then:

  1. O divides GH in the ratio 1 : 2

  2. G divides OH in the ratio 1 : 2

  3. H divides OG in the ratio 1 : 2

  4. O divides GH in the ratio 2 : 1
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B Correct answer
Explanation

In any triangle, the centroid G lies on the Euler line between the circumcentre O and the orthocentre H, dividing the segment OH in the ratio 1:2.

AI explanation

According to Euler's theorem, the centroid, orthocentre and circumcentre of a triangle are collinear, lying on the Euler line. The centroid acts as the balancing point of this system, meaning it divides the line segment joining the orthocentre and the circumcentre internally in a ratio of 2 to 1 from the orthocentre. This means G divides OH in the ratio 1 to 2.

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