# Geometry

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Question

Suppose that triangle ABC is obtuse, i.e., it has one angle which is greater than ninety degrees. Prove that its circumcentre is outside the triangle. (Hint: it is probably easier to prove the contrapositive statement: if trangle ABC is a triangle whose circumcentre is inside the triangle, then it is an acute-angled triangle. The statement and the contrapositive are logically equivalent, so proving one, also proves the other.)