Computable Euclid

Statement

Statement HTML

To inscribe a circle in a given triangle.

Construction steps

Construction Steps HTML

Let △ABC be the given triangle.

Bisect ∠CAB and ∠CBA. These two angle bisectors intersect at O.

From O, draw a line that is perpendicular to AB and name the intersection D.

Construct the circle through the point D centered at O. the circle through the point D centered at O has been inscribed in the given △ABC.

Computable version

In[1]:=

GeometricSceneA.,B.,C.,O.,D.,{},GeometricStepTriangleA.,B.,C.,GeometricStepInfiniteLineA.,O.AngleBisectorC.,A.,B.,InfiniteLineB.,O.AngleBisectorC.,B.,A.,GeometricStepGeometricAssertionLineO.,D.,Line[A.,D.,B.],"Perpendicular",GeometricStepCircleThroughD.,O.,CircleThroughD.,O.//RandomInstance

Out[]=

PlaneGeometry`GeometrySceneDrawerDump`makeGraph

icsFromRulesAbsoluteThickness[2],

,

EdgeForm[{

,

Thickness[Large]}],Opacity[0.2],

Polygon



GeometricPoint

A.,



GeometricPoint

B.,



GeometricPoint

C.,Dashing[{Small,

Small}],CapForm[None],

Line



GeometricPoint

C.,



GeometricPoint

A.,Dashing[{Small,

Small}],CapForm[None],

Line



GeometricPoint

A.,



GeometricPoint

B.,Dashing[{Small,

Small}],CapForm[None],

Line



GeometricPoint

C.,



GeometricPoint

B.,Dashing[{Small,

Small}],CapForm[None],

Line



GeometricPoint

B.,



GeometricPoint

A.,Line



GeometricPoint

O.,



GeometricPoint

D.,Line



GeometricPoint

A.,



GeometricPoint

B.,InfiniteLine



GeometricPoint

A.,-



GeometricPoint

A.[1]+



GeometricPoint

O.[1],-



GeometricPoint

A.[2]+



GeometricPoint

O.[2],InfiniteLine



GeometricPoint

B.,-



GeometricPoint

B.[1]+



GeometricPoint

O.[1],-



GeometricPoint

B.[2]+



GeometricPoint

O.[2],Circle



GeometricPoint

O.,



GeometricQuantity





Unspecified

radius,

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

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

"{4, 1, 0}", "1"]], C["Geometric

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

"{4, 1, 0}", "2"]]}, {4, 1,

0}},

,AbsolutePointSize[17],

Point



GeometricPoint

O.,Inset O. ,



GeometricPoint

O.,AbsolutePointSize[17],

Opacity[0],Point



GeometricPoint

O.,

,

AbsolutePointSize[17],

Point



GeometricPoint

D.,Inset D. ,



GeometricPoint

D.,AbsolutePointSize[17],

Opacity[0],Point



GeometricPoint

D.,

,

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

C.,Inset C. ,



GeometricPoint

C.,AbsolutePointSize[17],

Opacity[0],

Point



GeometricPoint

C.,{}



GeometricPoint

A.{-1.2988,

-2.5284},



GeometricPoint

B.{-0.126222,

3.68466},



GeometricPoint

C.{3.68985,

4.95498},



GeometricPoint

D.{-0.251489,

3.02091},



GeometricPoint

O.{0.877581,

2.80782},



GeometricPoint





Unspecified

ref,

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

C["GeometricPoint"][A.],

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

1{-1.36435,-2.68912},



GeometricPoint





Unspecified

ref,geoAngleBisecto

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

C["GeometricPoint"][A.],

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

2{-1.2988,-2.5284},



GeometricPoint





Unspecified

ref,geoAngleBisecto

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

C["GeometricPoint"][B.],

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

1{0.00440609,3.57056},



GeometricPoint





Unspecified

ref,geoAngleBisecto

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

C["GeometricPoint"][B.],

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

2{-0.126222,

3.68466},



GeometricQuantity





Unspecified

radius,

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

oint"][C["Unspecified"]["ref", "{4,

1, 0}", "1"]], C["GeometricPoint"

][C["Unspecified"]["ref", "{4, 1,

0}", "2"]]}, {4, 1, 0}}1.149

Last updated on: 2022-03-04.

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

Euclid Book 4

Proposition 4

Construction

Statement

Statement HTML

Construction steps

Construction Steps HTML

Original statement

ϵἰς τὸ δοθὲν τρίγωνον κύκλον ἐγγράψαι.

English translation

In a given triangle to inscribe a circle.

Computable version

Additional instances

Dependency graphs

Classes

Euclid Book 4

Proposition 4

Construction

Statement

Statement HTML

Construction steps

Construction Steps HTML

Original statement

ϵἰς τὸ δοθὲν τρίγωνον κύκλον ἐγγράψαι.

English translation

In a given triangle to inscribe a circle.

Computable version

Additional instances

Dependency graphs

Classes

Related theorems