Square covering disk

Question

This question comes from TOT Fall 2017 Senior A Level.

Is it possible to cut the 1 × 1 square into two parts which can cover a disk of diameter greater than 1?

Any help will be appreciated. Thanks

Answer 1

The picture below gives a possible answer: the brown piece is cut out of the square and moved to a new position (gray) to cover the two small circle segments lying outside the square.

Answer 2

On the rule, each figures never overlap.

Note 1 the number of circles are $1,4,9,16$ is optimal packing.

Those divisions include just circle with diameter 1. Therefore it's impossible.