in triangle ABC ,AB=13,BC=14,CA=15 . find the length of tangent from A to circle drawn with BC as diameter

Dear ajinkya

length of median of triangle AO  = 1/2 √(2b²+2c² -a²)

                                              = 1/2 √(592

                                              =2√37

so AT² =AO² -TO²

          =4*37 - 49

         =99

AT =3√11

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