一個圓內接梯形,同時外接正方形,求正方形面積

......................3
..............A─────B
........3.../..|............|.3
............/...|.....O....|...\
.......D./──────── C
...............d.....4....c
O 為外接圓心 , 故外接圓半徑 r = OA = OB = OC = OD。設 Ad ⊥ DC 及 Bc ⊥ DC
則 Dd = Cc = (DC - AB) / 2 = (4 - 3)/2 = 1/2故梯形高 Ad = √(AD² - Dd²) = √(3² - (1/2)²) = √35 / 2
又梯形高為 √(OA² - (AB/2)²) + √(OD² - (DC/2)²) = √(r² - (3/2)²) + √(r² - (4/2)²)得
√(r² - (3/2)²) + √(r² - (4/2)²) = √35 / 2
(r² - 9/4) + (r² - 4) + 2√((r² - 9/4)(r² - 4)) = 35/4
2√((r² - 9/4) (r² - 4)) = 35/4 - 2r² + 9/4 + 4
2√((r² - 9/4) (r² - 4)) = 15 - 2r²
4r⁴- 25r² + 36 = 4r⁴- 60r² + 225
r² = 27/5 正方形面積 = (2r)² = 4r² = 108/5

You can try to set coordinate.