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Question

In â–³ABC, if 1a+b+1a+c=3a+b+c then

A
A=60o
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B
B=60o
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C
C=60o
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D
A=90o
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Solution

The correct option is A A=60o
1a+b+1a+c=3a+b+c
2a+b+ca2+ab+ac+bc=3a+b+c
(2a+b+c)(a+b+c)=3(a2+ab+ac+bc)
2a2+2ab+2ac+ab+b2+bc+ac+bc+c2
=3a2+3ab+3ac+3bc
a2=b2+c2bc
cosA=b2+c2a22bc
=b2+c2b2c2+bc2bc
cosA=12
Also, cos60=12
on comparing angles
A=60

1180216_1284074_ans_f16a3c4323094a0caeb7c64b5f8fdd46.jpg

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