Puzzle of the Week #73 - Walk in the Park

There is a circular park with a radius of 200m. I want to build a circular lake of radius 91m inside the park.

I wish to be able to walk from a point on the edge of the park, on a straight line tangential to the lake, until I meet the edge of the park again, and then do the same twice more and end up where I started.

If I place the lake centrally in the park, I will go past my original point on the circumference.

If I place it too far from the centre of the park, I will not get all the way round to my starting point.

How far from the centre of the park should the centre of the lake be to ensure that I end up precisely where I started?