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

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

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7 years ago
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