Observe the line segments with the same color in the picture, and the following formula holds.

2r+c=a+b, both sides are squared at the same time,

Get 4r 2+4r c 2 = a 2+2ab+b 2.

∫a2+B2 = C2 Here we go again

The above formula is simplified as 2r 2+2r c = ab.

∴△ area = r 2+RC

The area ratio is option B.