A circle of radius R inscribes three circles of radius T
Find T in terms of R
I have found that the three circles with radius T form an equilateral triangle
The answer is supposed to be T=0.464R
If we connect the vertices of that equilateral triangle into the center we have the radius point of the larger circle. Then, we create 3 isosceles triangles.
Each of these triangles we can use the law of cosines.
But a=b, so:
Then radius of the large circle is R, so we have:
Solve for T and we have: