A circle touches the side BC of a $$\triangle$$ABC at P and also touches AB and AC produced at Q and R, respectively. If the perimeter of $$\triangle$$ABC = 26.4 cm, then the length of AQ is:

From the given question we draw the diagram is given below 

From the above diagram 

AQ = AR (from A)  (Length drown from external tangent in equal)

BQ = BP (from B)

CP=CR (from C) 

Perimeter of $$\triangle ABC = AB +BC+CA $$

                                           = AB + (BP+PC) + (AR-CR) 

Perimeter of $$\triangle ABC = (AB+BQ)+(PC)+(AQ-PC) $$

(Using the value AQ=AR, BQ=BP, CP=CR)

Perimeter of $$\triangle = 2AQ $$

$$\Rightarrow AQ= \frac{1}{2}\times perimeter  of   \triangle ABC $$

 $$\Rightarrow AQ = \frac{1}{2} \times 26.4 $$

                            = $$\frac 13.2 cm $$Ans