** The radius of the incircle of a triangle is 4 cm and the segments into which one side is divided by the point of contact are 6cm and 8 cm .Determine the other two sides of the triangle.**

** **

**Let the given circle touch the sides AB and AC of the triangle at point E and F respectively and the length of the line segment AF be x.**

**In ABC,**

**CF = CD = 6cm (Tangents on the circle from point C)**

**BE = BD = 8cm (Tangents on the circle from point B)**

**AE = AF = x (Tangents on the circle from point A)**

**AB = AE + EB = x + 8**

**BC = BD + DC = 8 + 6 = 14**

**CA = CF + FA = 6 + x**

**2 s = AB + BC + CA**

**= x + 8 + 14 + 6 + x**

*=* 28 + 2*x*

*s* = 14 + *x*

**Area of ΔOBC = **

**Area of ΔOCA =**

**Area of ΔOAB =**

**Area of ΔABC = Area of ΔOBC + Area of ΔOCA + Area of ΔOAB**

**Either x+14 = 0 or x − 7 =0**

**Therefore , x = −14and 7**

**However, x = −14 is not possible as the length of the sides will be negative.**

**Therefore, x = 7**

**Hence, AB = x + 8 = 7 + 8 = 15 cm**

**CA = 6 + x = 6 + 7 = 13 cm**

**THUMBS UP PLEASE.**