Computable Euclid

Statement

Statement HTML

To circumscribe a circle about a given triangle.

Construction steps

Construction Steps HTML

Let △ABC be the given triangle.

Construct the perpendicular bisector of CA and the perpendicular bisector of CB. Let O be the intersection of these two lines.

Construct the circle through the point A centered at O. This circle has been circumscribed about the given △ABC.

Computable version

In[1]:=

GeometricSceneA.,B.,C.,O.,{},GeometricStepTriangleA.,B.,C.,GeometricStepGeometricAssertionPerpendicularBisectorC.,A.,PerpendicularBisectorC.,B.,"Concurrent",O.,GeometricStepCircleThroughA.,O.,CircleThroughA.,O.//RandomInstance

Out[]=

PlaneGeometry`GeometrySceneDrawerDump`makeGraph

icsFromRulesAbsoluteThickness[2],

,

EdgeForm

,

Thickness[Large],Opacity[0.2],

Polygon



GeometricPoint

A.,



GeometricPoint

B.,



GeometricPoint

C.,PlaneGeometry`Geomet

rySceneDrawerDump`makeAngleGraphicsPlaneG

eometry`GeometrySceneDrawerDump`geoAngle



GeometricPoint

C.,



GeometricPoint





Unspecified

ref,geoPerpendicu

larBisector[{C["GeometricPoint"][C.],

C["GeometricPoint"][A.]}],1,



GeometricPoint





Unspecified

ref,geoPerpendicu

larBisector[{C["GeometricPoint"][C.],

C["GeometricPoint"][A.]}],2

π

2

,P

laneGeometry`GeometrySceneDrawerDump`makeA

ngleGraphicsPlaneGeometry`GeometrySceneDr

awerDump`geoAngle



GeometricPoint

C.,



GeometricPoint





Unspecified

ref,geoPerpendicu

larBisector[{C["GeometricPoint"][C.],

C["GeometricPoint"][B.]}],1,



GeometricPoint





Unspecified

ref,geoPerpendicu

larBisector[{C["GeometricPoint"][C.],

C["GeometricPoint"][B.]}],2

π

2

,Dashing[{Small,Small}],

CapForm[None],Line



GeometricPoint

C.,



GeometricPoint

A.,Dashing[{Small,

Small}],CapForm[None],

Line



GeometricPoint

C.,



GeometricPoint

B.,InfiniteLine



GeometricPoint





Unspecified

ref,

geoPerpendicularBisector[{C["GeometricPoint"][C.],

C["GeometricPoint"][A.]}],1,-



GeometricPoint





Unspecified

ref,geoPerpendic

ularBisector[{C["GeometricPoint"][C.],

C["GeometricPoint"][A.]}],1[1]+



GeometricPoint





Unspecified

ref,geoPerpendic

ularBisector[{C["GeometricPoint"][C.],

C["GeometricPoint"][A.]}],2[1],-



GeometricPoint





Unspecified

ref,geoPerpendic

ularBisector[{C["GeometricPoint"][C.],

C["GeometricPoint"][A.]}],1[2]+



GeometricPoint





Unspecified

ref,geoPerpendic

ularBisector[{C["GeometricPoint"][C.],

C["GeometricPoint"][A.]}],

2[2],InfiniteLine



GeometricPoint





Unspecified

ref,

geoPerpendicularBisector[{C["GeometricPoint"][C.],

C["GeometricPoint"][B.]}],1,-



GeometricPoint





Unspecified

ref,geoPerpendic

ularBisector[{C["GeometricPoint"][C.],

C["GeometricPoint"][B.]}],1[1]+



GeometricPoint





Unspecified

ref,geoPerpendic

ularBisector[{C["GeometricPoint"][C.],

C["GeometricPoint"][B.]}],2[1],-



GeometricPoint





Unspecified

ref,geoPerpendic

ularBisector[{C["GeometricPoint"][C.],

C["GeometricPoint"][B.]}],1[2]+



GeometricPoint





Unspecified

ref,geoPerpendic

ularBisector[{C["GeometricPoint"][C.],

C["GeometricPoint"][B.]}],

2[2],Circle



GeometricPoint

O.,



GeometricQuantity





Unspecified

radius,

{{C["GeometricPoint"][A.], C["Geometri

cPoint"][C["Unspecified"]["ref",

"{3, 1, 0}", "1"]], C["Geometric

Point"][C["Unspecified"]["ref",

"{3, 1, 0}", "2"]]}, {3, 1,

0}},

,AbsolutePointSize[17],

Point



GeometricPoint

C.,Inset C. ,



GeometricPoint

C.,AbsolutePointSize[17],

Opacity[0],Point



GeometricPoint

C.,

,

AbsolutePointSize[17],

Point



GeometricPoint

A.,Inset A. ,



GeometricPoint

A.,AbsolutePointSize[17],

Opacity[0],Point



GeometricPoint

A.,

,

AbsolutePointSize[17],

Point



GeometricPoint

B.,Inset B. ,



GeometricPoint

B.,AbsolutePointSize[17],

Opacity[0],Point



GeometricPoint

B.,

,

AbsolutePointSize[17],

Point



GeometricPoint

O.,Inset O. ,



GeometricPoint

O.,AbsolutePointSize[17],

Opacity[0],

Point



GeometricPoint

O.,{}



GeometricPoint

A.{1.12275,

-1.05045},



GeometricPoint

B.{4.15193,

4.76999},



GeometricPoint

C.{0.42485,

2.12856},



GeometricPoint

O.{3.86929,

1.21862},



GeometricPoint





Unspecified

ref,geoPe

rpendicularBisector[{C["GeometricPoint"

][C.], C["GeometricPoint"][A.]}],

1{0.7738,0.539055},



GeometricPoint





Unspecified

ref,geoPerpendicula

rBisector[{C["GeometricPoint"][C.],

C["GeometricPoint"][A.]}],2{1.75054,

0.753482},



GeometricPoint





Unspecified

ref,geoP

erpendicularBisector[{C["GeometricPoint

"][C.], C["GeometricPoint"][B.]}],

1{2.28839,3.44928},



GeometricPoint





Unspecified

ref,geoPerpendicula

rBisector[{C["GeometricPoint"][C.],

C["GeometricPoint"][B.]}],2{2.86661,

2.6334},



GeometricQuantity





Unspecified

radius,

{{C["GeometricPoint"][A.], C["GeometricP

oint"][C["Unspecified"]["ref", "{3,

1, 0}", "1"]], C["GeometricPoint"

][C["Unspecified"]["ref", "{3, 1,

0}", "2"]]}, {3, 1, 0}}

3.5626

Last updated on: 2022-03-04.

A collection of classical geometry in computable formats along with code and diagrams.

Euclid Book 4

Proposition 5

Construction

Statement

Statement HTML

Construction steps

Construction Steps HTML

Original statement

πϵρὶ τὸ δοθὲν τρίγωνον κύκλον πϵριγράψαι.

English translation

About a given triangle to circumscribe a circle.

Computable version

Additional instances

Dependency graphs

Classes

Euclid Book 4

Proposition 5

Construction

Statement

Statement HTML

Construction steps

Construction Steps HTML

Original statement

πϵρὶ τὸ δοθὲν τρίγωνον κύκλον πϵριγράψαι.

English translation

About a given triangle to circumscribe a circle.

Computable version

Additional instances

Dependency graphs

Classes

Related theorems