The lengths of three sides of triangle ABC are a, B, C, and a > b > C, ABC are positive integers, satisfying the condition of 1 / A + 1 / B + 1 / C = 1. Try to judge whether triangle ABC exists, and explain the reason

The lengths of three sides of triangle ABC are a, B, C, and a > b > C, ABC are positive integers, satisfying the condition of 1 / A + 1 / B + 1 / C = 1. Try to judge whether triangle ABC exists, and explain the reason

Such triangles do not exist
a> B > C, 1 / A + 1 / B + 1 / C = 11, C1 / C = 1, so C = 2, then positive integers a and B must satisfy 1 / A + 1 / b = 1-1 / C = 1-1 / 2 = 1 / 2, and a > b > 2 = C, if B = 3, then a = 6, then 1 / A + 1 / B + 1 / C = 1 / 6 + 1 / 3 + 1 / 2 = 1, but 6 > 3 + 2 = 5, that is, three line segments with length of 6, 3 and 2 cannot form a triangle, so b > 3, if B = 4, then a = 4 will be deduced from 1 / A + 1 / b = 1 / 2, which is inconsistent with the condition a > b, and then if b > 4, a will be obtained

It is known that the lengths of ABC on three sides of a triangle are integers, and a is less than or equal to B and less than C. If b = 6, how many triangles are there

a. B and C are 2,6,7; 3,6,7; 3,6,8; 4,6,7; 4,6,8; 4,6,9; 5,6,7; 5,6,8; 5,6,9; 5,6,10; 6,6,7; 6,6,8; 6,6,9; 6,6,10; 6,6,11