MathLabs

Problem 2

Prove that if n≥4n\ge4, every quadrilateral that can be inscribed in a circle can be dissected into nn quadrilaterals each of which is inscribable in a circle.
Step 4 of 4: Reach every n≥4n\ge4
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In plain words

Each parallel cut adds exactly one valid cyclic piece.

n=4+k (k≥0)n=4+k\ (k\ge0)
Detailed analysis

Cut one isosceles trapezoid, say AEPHAEPH, by kk lines parallel to its bases. It becomes k+1k+1 cyclic trapezoids, so the total is 3+(k+1)=4+k=n3+(k+1)=4+k=n.