AngleBisector

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`AngleBisector`

[Experimental]

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AngleBisector[{q₁,p,q₂}]

gives the bisector of the interior angle at p formed by the triangle with vertex points p, q₁ and q₂.

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AngleBisector[{q₁,p,q₂},"type"]

gives the angle bisector of the specified type.

Details

AngleBisector gives an InfiniteLine object.
The q_i and p in AngleBisector[{q₁,p,q₂}] can be lists of coordinates or explicit Point objects.
AngleBisector[p{q₁,q₂}] is equivalent to AngleBisector[{q₁,p,q₂}].
AngleBisector gives the line that divides the angle into two equal angles and that passes through the point p.

The following bisector type specifications "type" can be given:
"Interior" bisector of the interior angle of the triangle at p

"Exterior" bisector of the exterior angle of the triangle at p
AngleBisector only works in 2D.
AngleBisector can be used with symbolic points in GeometricScene.

Examples

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Basic Examples (1)Summary of the most common use cases

Calculate an angle bisector:

In[1]:=1

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https://wolfram.com/xid/0fq65i2z32j0u-hi7kyk

Out[1]=1

In[2]:=2

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https://wolfram.com/xid/0fq65i2z32j0u-e61lmr

Out[2]=2

Scope (2)Survey of the scope of standard use cases

Find an interior angle bisector:

In[1]:=1

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https://wolfram.com/xid/0fq65i2z32j0u-86fb9m

Out[1]=1

Find an exterior angle bisector:

In[1]:=1

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https://wolfram.com/xid/0fq65i2z32j0u-4a7ghx

Out[1]=1

Properties & Relations (4)Properties of the function, and connections to other functions

AngleBisector finds the interior angle bisector by default:

In[1]:=1

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https://wolfram.com/xid/0fq65i2z32j0u-ybhc

Out[1]=1

In[2]:=2

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https://wolfram.com/xid/0fq65i2z32j0u-i7i7wo

Out[2]=2

The angle bisector divides the angle into two equal angles:

In[1]:=1

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https://wolfram.com/xid/0fq65i2z32j0u-gda6u4

Out[1]=1

In[2]:=2

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https://wolfram.com/xid/0fq65i2z32j0u-5iw9ao

Out[2]=2

In[3]:=3

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https://wolfram.com/xid/0fq65i2z32j0u-201o02

Out[3]=3

In[4]:=4

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https://wolfram.com/xid/0fq65i2z32j0u-3pml7s

Out[4]=4

The exterior angle bisector divides the exterior angle into two equal angles:

In[1]:=1

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https://wolfram.com/xid/0fq65i2z32j0u-qlwr32

Out[1]=1

In[2]:=2

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https://wolfram.com/xid/0fq65i2z32j0u-5u2htu

Out[2]=2

In[3]:=3

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https://wolfram.com/xid/0fq65i2z32j0u-lm6ofl

Out[3]=3

In[4]:=4

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https://wolfram.com/xid/0fq65i2z32j0u-zheqb4

Out[4]=4

TriangleConstruct[{a,b,c},"AngleBisector"] is equivalent to AngleBisector[{a,b,c}]:

In[1]:=1

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https://wolfram.com/xid/0fq65i2z32j0u-qdoui3

Out[1]=1

In[2]:=2

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https://wolfram.com/xid/0fq65i2z32j0u-m7u0mi

Out[2]=2

Possible Issues (2)Common pitfalls and unexpected behavior

The three points must be distinct:

In[1]:=1

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https://wolfram.com/xid/0fq65i2z32j0u-8xpomj

Out[1]=1

AngleBisector only works in 2D:

In[1]:=1

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https://wolfram.com/xid/0fq65i2z32j0u-119biw

Out[1]=1

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