A circle is inscribed in a rectangular trapezoid ABCD, the radius OE drawn to the side of CD divides it by CE

A circle is inscribed in a rectangular trapezoid ABCD, the radius OE drawn to the side of CD divides it by CE = 9 ED = 16, find the area of the trapezoid.

S (ABCD) = ((AD + BC) / 2) * H = ((AB + CD) / 2) * 2r = (2r + CD) * r = (2r + 25) * r.
AD + BC = AB + CD for the circumscribed quadrilateral
∠СOD = 180 ° – (∠OCD + ∠ODC) = 180 ° – (∠BCD / 2 + ∠ADC / 2) = 180 ° – (∠BCD + ∠ADC) / 2 = 180 ° -180 ° / 2 = 90 °.
From ΔCOD: (OE⊥CD); r = OE = √ (CO * DO) = √ (9 * 16) = 12.
S (ABCD) = (2r +25) * r = (2 * 12 +25) * 12 = 49 * 12 = 588.