In the xy-plane, what is the length of the shortest path from (0,0) to (12, 16) that does not go inside the circle (x-6) ^2+(y-8) ^2 = 25?

Since it cannot be inside the circle it can be tangent to the circle hence the distance can be calculated by joinning 0,0to centre of circle and (12,6 )to to centre as tangent is perpendicular to centre so we can calculte distance using pythagorus theorum on both the triangle and the answer will be 10√3

The answer is 10√3+5π/3 Since the two distance can be calculated by pythagorus theorum and third distance bycan be calculated by angle at the centre and radius so the ultimately answer is 10√3+5π/3