When the addenda on pinion and wheel is such that the path of approach and path of recess are half of their maximum possible values, then the length of the path of contact is given by (where r = Pitch circle radius of pinion, R = Pitch circle radius of wheel and $$\varphi $$ = Pressure angle)

A. $$\frac{{\left( {{{\text{r}}^2} + {{\text{R}}^2}} \right)\cos \varphi }}{2}$$

B. $$\frac{{\left( {{{\text{r}}^2} + {{\text{R}}^2}} \right)\sin \varphi }}{2}$$

C. $$\frac{{\left( {{\text{r}} + {\text{R}}} \right)\cos \varphi }}{2}$$

D. $$\frac{{\left( {{\text{r}} + {\text{R}}} \right)\sin \varphi }}{2}$$

Answer: Option D