Consider a circle with centre O and a point P lying outside the circle. The lines PA and PB touch the circle at the points A and B respectively.
(i) Define a tangent to a circle.
(ii) Give a geometrical reason to show that ∠OAP=90∘.
(iii) Using suitable reasoning, explain why PA=PB. Treat this result entirely as a consequence of right–angle properties obtained in part (ii).