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circumference(a)=6.28=2(pi)r, yields r(a)=1
area(b)=12.56=(pi)r^2, yields r(b)=2
let the intersection of the line between the centers and the tangent line be point C.
For each circle, the center, the point of tangency, and C form a right triangle. The two triangles are mathematically similar.
Call each triangle by the same letter as the circle whose center it contains. Thus triangle A:triangle 2 is 1:2.
The hypotenuse of triangle A plus the hypotenuse of triangle B equals 5. Additionally, hypotenuse B is twice hypotenuse A. Thus, hypotenuse A is 5/3
Angle is determined by inverse sine; opposite over adjacent.
sin^(-1)(a/c)=sin^(-1)(3/5)=36.8698976 degrees or 0.643501109 radians
Basically, the tangent line, the line between the centers, and the radii form a pair of 3:4:5-ratio right triangles.
area(b)=12.56=(pi)r^2, yields r(b)=2
let the intersection of the line between the centers and the tangent line be point C.
For each circle, the center, the point of tangency, and C form a right triangle. The two triangles are mathematically similar.
Call each triangle by the same letter as the circle whose center it contains. Thus triangle A:triangle 2 is 1:2.
The hypotenuse of triangle A plus the hypotenuse of triangle B equals 5. Additionally, hypotenuse B is twice hypotenuse A. Thus, hypotenuse A is 5/3
Angle is determined by inverse sine; opposite over adjacent.
sin^(-1)(a/c)=sin^(-1)(3/5)=36.8698976 degrees or 0.643501109 radians
Basically, the tangent line, the line between the centers, and the radii form a pair of 3:4:5-ratio right triangles.
