Online Geometry theorems, problems, solutions, and related topics.
See complete Problem 95Similar Triangles, Inradii, Parallel. Level: High School, SAT Prep, College geometryPost your solutions or ideas in the comments.
Just saw the problem on the Mathematica Blog and followed the Mathematica Demo athttp://demonstrations.wolfram.com/TheRadiiOfFourIncircles/ So I wondered why it was true. Placing the radii of the incircles to the tangent points on BC and using similar triangles makes it clear:r/BC=r1/BE =r2/EG =r3/GC=(r1+r2+r3)/(BE+EG+GC).Since (BE+EG+GC=BC), r = r1+r2+r3.