Calculate 70% of the area inside a polygon based on the polygon centroid

I am trying to generate an area within a polygon based on the polygons centroid that covers 70% of the containing polygons area. I generated the polygon centroids as points but I do not know how to generate a buffer based on both the polygon centroid as the start of the buffer location and constraining the desired polygon to be 70% of the original polygon size.

FYI - polygons are parcels

• You can find radius by solving circle area equation. Will not work for skinny parcels though. Mar 2, 2020 at 19:16
• Use a negative buffer on the polygon. You can make a binary search algorithm to iteratively buffer by some prorated fraction so that the buffer approaches exactly 70%. I've done this in the past, and it's somewhat comptutationally prolifigate, but if you only require 99% accuracy it doesn't take more than a score of iterations; Four nines can usually be accomplished in 100-120 iterations. Mar 3, 2020 at 0:31
• If it's not about centroid, little modifications of gis.stackexchange.com/questions/215813/… will get you there. Mar 3, 2020 at 4:06