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 1 of 4: Use the cyclic criterion
In plain words

This criterion reduces the construction to matching angles.

∠A+∠C=π⟺ABCD is cyclic\angle A+\angle C=\pi\Longleftrightarrow ABCD\text{ is cyclic}
Detailed analysis

A quadrilateral is cyclic exactly when a pair of opposite angles is supplementary. In particular, every isosceles trapezoid is cyclic.