find the insimilitude and outsimilitude of two circles - Maple Help

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geometry[similitude] - find the insimilitude and outsimilitude of two circles

Calling Sequence

similitude(obj, c1, c2)

Parameters

obj

-

name which is assigned the internal and external centers of similitude

c1, c2

-

two circles

Description

• 

Let c1=Aa and c2=Bb be two nonconcentric circles and let I and E divide SensedMagnitude(AB) internally and externally in the ratio a/b. Then I and E are called the internal and the external centers of similitude of the two circles c1 and c2

• 

The routine assigns to obj a list of two elements where the first element is the internal center of similitude, and then second element the external center of similitude.

• 

For a detailed description of the centers of similitude obj, use the routine detail (i.e., detail(obj))

• 

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

Examples

withgeometry:

_EnvHorizontalName:='x':_EnvVerticalName:='y':

circlec1,x2+y2=1,circlec2,pointA,3,3,4:

circlec3,x22+y2=1:

similitudeobj1,c1,c2

in_similitude_of_c1_c2,ex_similitude_of_c1_c2

(1)

mapcoordinates,obj1

35,35,1,1

(2)

similitudeobj2,c1,c3,M,N

similitude:   "hint: the external and internal centers of similitude are the same"

M,N

(3)

detailobj2

name of the objectMform of the objectpoint2dcoordinates of the point1,0,name of the objectNform of the objectpoint2dcoordinates of the point1,0

(4)

See Also

geometry[CircleOfSimilitude], geometry[HorizontalName], geometry[SensedMagnitude], geometry[VerticalName]


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