Source — Euclid's Elements, encoded as an rrxiv paper

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About a given square to circumscribe a circle.

Join the diagonals

A C

and

B D

of the given square, intersecting at

E

. In the right triangles

△ A B E

and

△ A D E

, SSS (I.8) gives

∠ E A B = ∠ E A D

, so

A E

bisects the right angle at

A

; similarly at every vertex. The four triangles at

E

are then isosceles with equal vertex angles (I.6), so

E A = E B = E C = E D

. The circle with centre

E

and radius

E A

passes through all four vertices.