<Li> a 2 + b 2 + c 2 = a b + b c + c a (\ displaystyle \ displaystyle a ^ (2) + b ^ (2) + c ^ (2) = ab + bc + ca) </Li> <Li> a b c = (a + b − c) (a − b + c) (− a + b + c) (Lehmus) (\ displaystyle \ displaystyle abc = (a + b-c) (a-b + c) (- a + b + c) \ quad (\ text ((Lehmus)))) </Li> <Li> (a + b + c) (1 a + 1 b + 1 c) = 9 (\ displaystyle \ displaystyle (a + b + c) \! \ left ((\ frac (1) (a)) + (\ frac (1) (b)) + (\ frac (1) (c)) \ right) = 9) </Li> <Li> 1 a + 1 b + 1 c = 25 R r − 2 r 2 4 R r (\ displaystyle \ displaystyle (\ frac (1) (a)) + (\ frac (1) (b)) + (\ frac (1) (c)) = (\ frac (\ sqrt (25Rr - 2r ^ (2))) (4Rr))) </Li>

Distance from center to vertex of equilateral triangle