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King's Maths School

Challenge 431: An obtuse question

How likely are these angles?

ABCD is a rectangle with AB = 2 and BC = 1. X is a point inside the rectangle.

Of the four angles AXB, BXC, CXD and DXA, what is the maximum number that could be obtuse? What is the minimum number that could be obtuse?

If X is placed at random inside the rectangle, what is the probability that angle BXC is obtuse but the other three are acute?

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