find the Euler circle of a given triangle - Maple Help

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geometry[EulerCircle] - find the Euler circle of a given triangle

Calling Sequence

EulerCircle(Elc, T, 'centername'=cn)

Parameters

T

-

triangle

Elc

-

the name of the Euler circle

'centername' = cn

-

(optional) where cn is a name of the center of the Euler's circle.

Description

• 

The Euler circle Elc of triangle T is the circumcircle of the medial triangle of T

• 

Note that it was O. Terquem who named this circle the nine-point circle, and this is the name commonly used in the English-speaking countries. Some French geometers refer to it as Euler's circle, and German geometers usually call it Feuerbach's circle.

• 

If the third optional argument is given and is of the form 'centername' = cn where cn is name, cn will be the name of the center of Elc.

• 

For a detailed description of the Euler circle Elc, use the routine detail (i.e., detail(Elc))

• 

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

• 

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

Examples

withgeometry:

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

EulerCircleElc,T,'centername'=o

Elc

(1)

detailElc

assume that the names of the horizontal and vertical axes are _x and _y, respectively

name of the objectElcform of the objectcircle2dname of the centerocoordinates of the center1,56radius of the circle253636equation of the circle1+_x2+_y22_x53_y=0

(2)

medialT1,T:

drawT,T1,Elc,printtext=true

See Also

geometry[circle], geometry[medial], geometry[triangle]


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