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

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

Please feel free to post as many doubts on our discussion forum as you can. We are all IITians and here to help you in your IIT JEE preparation.

Win exciting gifts by answering the questions on Discussion Forum. So help discuss any query on askiitians forum and become an Elite Expert League askiitian.

Now you score 5+15 POINTS by uploading your Pic and Downloading the Askiitians Toolbar  respectively : Click here to download the toolbar..