Discs with radii of 3 cm and 4 cm are placed in the smallest equilateral triangle that can contain them, similar to Discs in a Triangle.

Then two more discs of equal radii are placed along with the 3 cm and 4 cm discs inside the same triangle. What is the largest radius that the new discs can have?

The smallest equilateral triangle has edge lengths 11sqrt3 and height 33/2. This means that the closest that the 4 cm circle gets to the edge that it doesn't touch is 9/2. There is definitely room for two circles of radius 9/4 cm. However, there is still a tiny amount of room to jostle these circles into the corner and away from that closest point, so a slightly larger radius is possible...

Posted by Pablo on 2020-07-31 11:53:05