<P> In an equilateral triangle, the altitudes, the angle bisectors, the perpendicular bisectors and the medians to each side coincide . </P> <P> A triangle ABC that has the sides a, b, c, semiperimeter s, area T, exradii r, r, r (tangent to a, b, c respectively), and where R and r are the radii of the circumcircle and incircle respectively, is equilateral if and only if any one of the statements in the following nine categories is true . Thus these are properties that are unique to equilateral triangles . </P> <Ul> <Li> a = b = c (\ displaystyle \ displaystyle a = b = c) </Li> <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> </Ul> <Li> a = b = c (\ displaystyle \ displaystyle a = b = c) </Li>

Which statements about finding the area of the equilateral triangle are true