An isosceles trapezoid problem

[MathBuster Forum]

A trapezoid is a four-sided figure with one pair of parallel sides. If the non-parallel sides are equal in length, the trapezoid is called an isosceles trapezoid.

Isosceles trapezoid ABCD has parallel sides AD and BC, and sides AB = DC = x. 

The area of the trapezoid is 510 sq. cm. A circle with centre O and radius 10 cm is inscribed in the trapezoid so that it is tangent to each of the four sides of the trapezoid. 

Determine the length of x.

Fact: A line drawn from the centre of a circle to the point where a tangent meets the circle is perpendicular to the tangent.