question_answer

A brick 2" thick is placed against a wheel to act for a stop. The horizontal distance of the face of the brick from the point where the wheel touches the ground is 6". The radius of the wheel (in inches) is -

A)  10                   

B)  5

C)  12                   

D)  6

Correct Answer: A

Solution :

 Suppose f be the radius of the circle PS - 6", QS = 2", In \[\Delta ORQ\] \[O{{Q}^{2}}=O{{R}^{2}}~+\text{ }R{{Q}^{2}}\Rightarrow ~{{r}^{2}}={{\left( r-2 \right)}^{2}}~+{{6}^{2}}\] \[\Rightarrow \] \[r{{~}^{2}}-{{\left( r-2 \right)}^{2}}~=36\Rightarrow ~4r-4=36\] \[\therefore \,\,\,\,\,\,\,\,\,\]