Question 78
Three non-intersecting circles of radius $1$ are placed inside the triangle $ABC$. (Circles can touch each other and the sides of a triangle, but cannot share interior points.)
Find the largest value of $r$ for which we can be sure that inside the triangle it is possible to draw a fourth circle of radius $r$ that doesn't intersect with three circles already drawn.
Find the largest value of $r$ for which we can be sure that inside the triangle it is possible to draw a fourth circle of radius $r$ that doesn't intersect with three circles already drawn.