Problem 5
In triangle ABC, points M and N lie on AB and AC, respectively, and MB=BC=CN. If R and r are the circumradius and inradius of ABC, express MN/BC in terms of R and r.
Step 4 of 5: Relate the desired ratio to OI
Detailed analysis
Since NC=BC and OD=R, the similarity gives MN/BC=OI/R.