If three sides ABC of triangle ABC satisfy (a-5) & sup2; + (B-12) & sup2; + C & sup2; = 26c-169, the shape of ABC is judged

（a-5)2+(b-12)2+(c-13)2=0
The lengths of the three sides are 5, 12 and 13 respectively
A triangle is a right triangle

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1. In triangle ABC, the corresponding sides of angle a, angle B and angle c are a, B and C respectively, and a & # 178; + B & # 178; + C & # 178; + 338 = 10A + 24B + 26c. Try to judge the shape of triangle ABC and prove it. (practice in the chapter of Pythagorean theorem, find the solution ~)
2. If the three sides of the triangle ABC are a, B, C and satisfy the following conditions: A2 + B2 + C2 + 338 = 10A + 24B + 26c, then the height of the longest side of the triangle ABC is () A. 8B. 125C. 6013D. 245
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