Soddy {LearnGeom}

Finds the inner and outer Soddy circles of three given mutually tangent circles

Description

Soddy finds inner and outer Soddy circles of three given mutually tangent circles

Usage

Soddy(A, r1, B, r2, C, r3)

Arguments

A

Vector containing the xy-coordinates of the center of circumference 1

r1

Radius for circumference 1

B

Vector containing the xy-coordinates of the center of circumference 2

r2

Radius for circumference 2

C

Vector containing the xy-coordinates of the center of circumference 3

r3

Radius for circumference 3

Value

A list which contains the Soddy center and the radiuses of Soddy inner and outer circle of three mutually tangent circles

References

http://mathworld.wolfram.com/SoddyCircles.html

Examples

x_min <- -3
x_max <- 3
y_min <- -2.5
y_max <- 3.5
CoordinatePlane(x_min, x_max, y_min, y_max)
A <- c(-1,0)
B <- c(1,0)
C <- c(0,sqrt(3))
r1 <- 1
r2 <- 1
r3 <- 1
Draw(CreateArcAngles(A, r1, 0, 360), "black")
Draw(CreateArcAngles(B, r2, 0, 360), "black")
Draw(CreateArcAngles(C, r3, 0, 360), "black")
result <- Soddy(A, r1, B, r2, C, r3)
soddy_point <- result[[1]]
inner_radius <- result[[2]]
outer_radius <- result[[3]]
Draw(soddy_point,"red")
Draw(CreateArcAngles(soddy_point,inner_radius,0,360),"red")
Draw(CreateArcAngles(soddy_point,outer_radius,0,360),"red")