Consider a circle with centre O and radius r. A point P lies outside the circle and a straight line l passes through P. The perpendicular distance from O to l is d. Answer the following:
a. (i) State the condition that must hold between d and r for the line l to be tangent to the circle.
b. (ii) Justify, with geometric reasoning, why the condition stated in part (i) is necessary and sufficient for l to be a tangent.
c. (iii) If r=4 cm and d=4 cm, what can you conclude about the position of l with respect to the circle? Explain your answer.