Stage: 5 Challenge Level: 
Mark a point $P$ inside a closed curve.
Is it always possible to find two points that lie on the curve, such that $P$ is the mid point of the line joining these two points?
Number theory. Generalising. Stage 5 - Reviewed 2012. Inequality/inequalities. Dynamical systems. Mathematical reasoning & proof. Rotations. Reflections. Visualising. Manipulating algebraic expressions/formulae.
Published July 2000.
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