Maths Olympiad Exam

Suppose five of the nine vertices of a regular nine-sided polygon are arbitrarily chosen. Show
that one can select four among these five such that they are the vertices of a trapezium.

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Maths Olympiad Other Question

Let D, E, F be points on the sides BC, CA, AB respectively of a triangle ABC such that
BD = CE = AF and BDF = CED = AFE. Prove that ABC is equilateral Let ABCD be a quadrilateral inscribed in a circle. Let E, F, G, H be the midpoints of the arcs AB, BC, CD, DA of the circle. Suppose AC· BD = EG · FH. Prove that AC, BD, EG, FH are concurrent.