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Question
Write the coordinates of the circumcentre of a triangle whose centroid and orthocentre are at (3, 3) and (−3, 5), respectively.
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Solution
Let the coordinates of the circumcentre of the triangle be C(x, y).
Let the points O(-3, 5) and G(3, 3) represent the coordinates of the orthocentre and centroid, respectively.
We know that the centroid of a triangle divides the line joining the orthocentre and circumcentre in the ratio 2:1.
\[\therefore 3 = \frac{- 3 \times 1 + 2x}{3}\text{ and }3 = \frac{5 \times 1 + 2y}{3}\]
\[ \Rightarrow x = 6, y = 2\]
Hence, the coordinates of the circumcentre is (6, 2).
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