Online Geometry theorems, problems, solutions, and related topics.
See complete Problem 94Similar Triangles, Circumradii, Parallel. Level: High School, SAT Prep, College geometryPost your solutions or ideas in the comments.
Triangles ABC,BDE,GFE&GMc are similar; hence ther circumradii will be proportional to their corresponding sides. Thus,R1/R=BE/BC,R2/R=GE/BC & R3/R=GC/BC. Or R1/R+R2/R+R3/R=(BG+EG+GC)/BC=BC/BC=1 or R1 + R2 + R3 = RAjit: firstname.lastname@example.org