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geometry

  

GergonnePoint

  

find the Gergonne point of a given triangle

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

GergonnePoint(G, ABC)

Parameters

G

-

the name of the Gergonne point

ABC

-

triangle

Description

• 

Let H, E, and F be the points of contact of the inscribed circle of triangle ABC with the sides BC, CA, AB respectively. AH, BE, CF are concurrent.

• 

The point of concurrency is called the Gergonne point of the triangle, after J. D. Gergonne (1771-1859), founder-editor of the mathematics journal Annales de mathematiques. Just why the point was named after Gergonne is not known.

• 

For a detailed description of the Gergonne point G, use the routine detail (i.e., detail(G))

• 

Note that the routine only works if the vertices of the triangle are known.

• 

The command with(geometry,GergonnePoint) allows the use of the abbreviated form of this command.

Examples

withgeometry:

triangleT,pointA,0,0,pointB,2,0,pointC,1,3:

GergonnePointG,T

G

(1)

detailG

name of the objectGform of the objectpoint2dcoordinates of the point1,310+101910+10

(2)

draw the picture of the above definition for the triangle T

incirclec,T:

segmentsg1,A,projectionH,centerc,linetmp,B,C:

segmentsg2,B,projectionE,centerc,linetmp,C,A:

segmentsg3,C,projectionF,centerc,linetmp,A,B:

drawsg1,sg2,sg3,ccolor=green,style=POINT,Gsymbol=DIAMOND,Tcolor=red,color=blue,printtext=true

See Also

geometry[point]

geometry[triangle]

 


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