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

About a given triangle to circumscribe a circle.

Let

A B C

be the given triangle. Bisect

A B

at

D

and

A C

at

E

(I.10). From

D

and

E

draw perpendiculars to

A B

and

A C

respectively (I.11), meeting at

F

. Join

F A

,

F B

,

F C

. By I.4 applied to the two right triangles at

D

,

F A = F B

; similarly at

E

,

F A = F C

. Thus

F A = F B = F C

, and the circle with centre

F

and radius

F A

passes through all three vertices.

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