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In a right triangle ABC, right-angled at B, it can be shown that the distance between the circumcentre and the centroid satisfies GD = (1/3)(BD) = (1/3)(AC/2), where D is the midpoint of the hypotenuse AC. If AC = 10, find GD.

1. 1
2. 5/3
3. 3
4. 10/3

Correct answer: 5/3

Solution

In a right triangle, the circumcentre is the midpoint of the hypotenuse, so BD = AC/2 = 5 (the median to the hypotenuse equals half the hypotenuse). Using the given relation GD = (1/3)(AC/2) = (1/3)(5) = 5/3.

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