Advanced Geometric Problem & Solution (Twice a week update) Now 4706 problems posted.
<Tri-2025-2279>, hint
Suppose line AM cuts the circumcircle of triangle ABC at N.
Then <ANB=<ACB hence triangles NKB and ABC are similar KN=KB
Since <ANC=<ABC <ACM=<AMC-<ANC=<ABC, Hence MN=MC.
KM+MC=KM+MN=KB
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