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Question

lf in a triangle ABC, a2+b2+c2=ca+ab3 , then the triangle is

A
equilateral
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B
right angled and isosceles
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C
right angled with one of the acute angles measuring π3
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D
obtuse angled
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Solution

The correct option is C right angled with one of the acute angles measuring π3
Given, a2+b2+c2=ac+ab3
=a(c+b3)

=2a(12c+b32)

=2a(ccos600+bcos300)=2a(ccosB+bcosC)
Hence
B=600 and C=300
Therefore
A=900.

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