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In a triangle if the lenght of the sides are a,b,c.then the given condition is a 2 +b 2 +c 2 =ab+bc+ca.then the triangle formed is a]right angled b]obtuse angled c]acute angled........[I want to know about the angle of the triangle ...so please help me to solve this problem]
a2+b2+c2 = ab+bc+ac (given) cosA = b2+c2-a2/2bc 2bccosA = b2+c2-a2 ...........1 2accosB = a2+c2-b2 ..........2 2abcosC = a2+b2-c2 .........3 adding 1,2,3 2(abcosC+bccosA+accosB) = a2+b2+c2 ........4 a2+b2+c2 = ab+bc+ac (given) so , 2(abcosC+bccosA+accosB) = ab+bc+ac 2ab(cosC-1/2) + 2bc(cosA-1/2) + 2ac(cosB-1/2) = 0 from this eq , cosC = cosA = cosB = 1/2 A=B=C = Pi/3 so the triangle is equilateral , acute angled triangle... approve if u like my ans
a2+b2+c2 = ab+bc+ac (given)
cosA = b2+c2-a2/2bc
2bccosA = b2+c2-a2 ...........1
2accosB = a2+c2-b2 ..........2
2abcosC = a2+b2-c2 .........3
adding 1,2,3
2(abcosC+bccosA+accosB) = a2+b2+c2 ........4
so , 2(abcosC+bccosA+accosB) = ab+bc+ac
2ab(cosC-1/2) + 2bc(cosA-1/2) + 2ac(cosB-1/2) = 0
from this eq , cosC = cosA = cosB = 1/2
A=B=C = Pi/3
so the triangle is equilateral , acute angled triangle...
approve if u like my ans
though this isnt the exact solution but if you are looking for answer directly the above condition satisifies when a=b=c,so it can be equilateral corresponds to the answer acute angled
though this isnt the exact solution but if you are looking for answer directly
the above condition satisifies when a=b=c,so it can be equilateral corresponds to the answer acute angled
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