<Tri-2025-2271>, hint

Let M be the midpoint of BC and M' on AB, M" on AC, MM'ㅗAB, MM"ㅗAC

Let <BAM=X <CBM=A-X , AM=MM'+MM''--->AM=AM(sinX+sin(A-X))

sinX+sin(A-X)=1---> 2 sin(A/2) cos(X-A/2)=1. Since cos(X-A/2)<=1, sin(A/2)>1/2

 THus <A>=60, Similarly <B>=60, <C>=60, A+B+C=180' Hence A=B=C=60