Online Geometry theorems, problems, solutions, and related topics.
See complete Problem 68Triangle, Incircle, Inradius, Tangent. Level: High School, SAT Prep, College geometryPost your solutions or ideas in the comments.
Let the equal circles at D & E touch AC in P & R resply. and let the bigger circle touch AC in Q. Triangles ADP and AOQ are similar and hence AP/AQ=d/r. Similarly CR/CQ =d/r. Thus,AP/AQ=CR/CQBut AP=AF & CR=CG so d/r = AF/AQ = CG/CQ = (AF+CG)/(AQ+CQ) = m/b or d/r = m/b or r = b*d/mAjit: email@example.com