I was shown this problem from a friend of mine, and it has been stuck in my head for a while now. I hope you can help me!
I am given three circles with given diameters and one triangle with given side lengths. My task is to figure out wether or not the three circles can be placed completely inside the triangle without overlapping each other.
Do you have an idea how to approach this?
Assuming a smaller circle ought not be placed inside a larger circle
(which would allow both smaller circles to be placed inside the larger one)
and also assuming you do not necessarily want them standing on a single line
(such as an x-axis)...
for example 2 of them on an axis and the third tangential to both of them.
Have you heard of the "First Ajima Malfatti Point" ?
That's an approach you can take.
If you place the circles on an x-y plane and use co-ordinate geometry, it can be checked
if the triangle is big enough.