If the three sides of a triangle form an arithmetic sequence, the circumference is 36 and the circumference of the inscribed circle is 6 π, then the triangle is a triangle

If the three sides of a triangle form an arithmetic sequence, the circumference is 36 and the circumference of the inscribed circle is 6 π, then the triangle is a triangle

I think it's a right triangle. If the three sides form an arithmetic sequence, then the length of the median side is 12. There's no doubt about that. The circumference of the inscribed circle is 6 π, so the radius of the inscribed circle is 3, which is not bad. The circumference of the triangle is 36
Suppose that the long side is 12 + D, the short side is 12-d, and the semi perimeter of the triangle P = 18
S = √ [P (P-A) (P-B) (P-C)], substituting the data, s = √ [18 * (6 + D) (6-D) * 6] = 6 √ [3 (36-d ^ 2)]
If the center of the inscribed circle divides the triangle into three parts, the edge is the bottom and the radius is the height, the area will be reduced
S = 0.5 [12 * 3 + 3 (12-d) + 3 (12 + D)] = 54, and d = 3 can be obtained by combining two area expressions
So the three sides of the triangle are 9, 12 and 15, that is, the original triangle is a right triangle