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Nirabhra Agrawal Grade: 12
        


If in a triangle ABC, a÷(b + c) = tan A/2, then show that the triangle is right angled.


6 years ago

Answers : (1)

AKASH GOYAL AskiitiansExpert-IITD
419 Points
										

Dear Nirabhra


Apply the formula



put s=(a+b+c)/2


then expression becomes


tanC/2=√(c+a-b)(a+b-c)/(a+b+c)(b+c-a) = √a2-(b-c)2/(b+c)2-a2


put the value of tanc/2= a/b+c and square both sides to get rid of root square


dont open the whole square terms like (b+c)2 and (b-c)2 as thy will cut after cross multiplication


after calculation you will get


a4=(b+c)2(b-c)2


a2=(b+c)(b-c)=b2-c2


b2=c2+a2


hence angle B is 90


 


All the best.                                                           


AKASH GOYAL


AskiitiansExpert-IITD


 


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6 years ago
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