Proposition IV.9 — About a given square to circumscribe a circle.

Proof

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.

Knowledge graph · drag to pan, scroll to zoom, click a node to navigate

Full neighborhood

Depends on (3)

I.6Proposition I.6If in a triangle two angles are equal to one another, the sides which subtend the equal angles will also be equal to…
I.8Proposition I.8If two triangles have the two sides equal to two sides respectively, and have also the base equal to the base, they…
I.15Definition I.15A circle is a plane figure contained by one line such that all the straight lines falling upon it from one point among…

Discussion

No replications, contradictions, or comments registered yet for this claim.

Replicate or annotate this claim

Replicate to register a fresh attempt; contradict, extend, or comment otherwise. Authors can post a claim-retraction with the reason taxonomy from RRP-0020.