CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

In ABC, the incircle touches the sides BC, CA and AB, respectively, D, E, and F. If the radius of the incircle is 4 units and BD, CE and AF are consecutive integers, then the value of s3, where s is a semi-perimeter of triangle, is

Open in App
Solution


Let BD=x,CE=x+1 and AF=x+2 Then
CD=CE=x+1=sc
AE=AF=x+2=sa
BF=BD=x=sb
On adding, we get
3s(a+b+c)=3x+3s=3x+3sa=x+2,sb=x,sc=x+1
Now, r=s=s(sa)(sb)(sc)
Or, 4=(x+2)x(x+1)3(x+1)
Or, x2+2x=48
x=6
Hence, s=21s3=7

flag
Suggest Corrections
thumbs-up
3
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Inradius and Exradius
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon