Image processing: How to find center of biggest blob in an image?
do a distance transform. you'll see why that's a good idea: for every pixel you get the shortest distance to a border. that's exactly the radius of an inscribed circle.

from this, just find the pixel with the largest value.

if you're curious, throw a "non-maximum suppression" on it. that is a kind of "morphological" kernel operation where you set a pixel to 0 if any neighbor has a strictly larger value.