in a triangle abc the incircle touches the sides bc,ca and ab respectively at d,e and f if the radius - Maths - Circles

Question

in a triangle abc the incircle touches the sides bc,ca and ab
respectively at d,e and f if the radius of the incircle is 4units
and if bd,ce and af are consecutive integers,find the sides of
triangle abc

Sukrit Gupta · Accepted Answer

Suppose that BD =
x, CE = x + 1 and AF = x + 2 Then CD =
CE = x + 1, AE = AF = x + 2, BF = BD =
x

Hence, a = BC =
x + x + 1 = 2x + 1,

b = CA = x
+ 1 + x + 2 = 2x + 3,

c = AB = x
+ 2 + x = 2x + 2;

Therefor x
= 6 and the side are a = 13 , b = 15 , c
= 14

in a triangle abc the incircle touches the sides bc,ca and ab respectively at d,e and f.if the radius of the incircle is 4units and if bd,ce and af are consecutive integers,find the sides of triangle abc