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The circumcentre and centroid of a trian...

The circumcentre and centroid of a triangle are `(3,4)` and `(6,8)` respectively. If one of the vertices of the triangle is `(0,0)`, then what is the type of triangle?

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We have vertex A(0,0) circumcentre O(3,4) and centroid G(6,8). Point O lies on the perpendicular bisector (OD) of side BC and point G lies on the median AD.
Now, A O and G are collinear. So median AD and perpendicular bisector (OD) of BC coincide. Thus, AD is the perpendicular bisector of BC. Therefore, triangle ABC is isosceles.
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