Krishna
0

Step 1: For better understanding construct a figure using the given data

            


Step 2: Look at the figure triangle OAP is right angle triangle. So use the Pythagoras theorem to find the length of the tangent (AP).

            NOTE:  Pythagoras theorem

                     (hypotenuses)^2 = (side)^2 + (side)^2

                  From the figure OAP

                     (AP)^2 = (OA)^2 + (AP)^2   


Step 3: Substitute all the known values in the theorem

                 (OP)^2 = (OA)^2 + (AP)^2

                (15)^2=9^2+(AP)^2    

                AP^2=225-81

                AP=\sqrt{144}

                              AP = 12