If in a triangle ABC, the exradii r₁, r₂, r₃ are such that r₁=2r₂=3r₃ then prove that the triangle is right angled . Also find a:b:c.

Dear student,
r1=2r2=3r3
Then
r1/6=r2/3=r3/2 =k using ratios
Hence r1=6k,
r2=3k
r3=2k
Hence using the property of solution of trianle the required triangle is equilateral.
Please feel free to ask your queries here. We are all IITians and here to help you in your IIT JEE preparation.
All the best.
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..

Askiitians Expert
Sagar Singh
B.Tech, IIT Delhi

Dear Sagar ji, 

Will you please solve this question in full as I could not prove the required results with the hints given by you. Few days back I had called and requested you for the same.Thanks.

G P Agrawal

F/o Nirabhra Agrawal

r1=6r by using a property 1/r1+1/r2+1/r3=1/rAs,r1=stanA/2, r=(s-a)tanA/2 ,So,s/(s-a)=6a=5s/6Similarly,b=2s/3,c=s/2,So,triangle is right angled at A