8.27 needs to find the area of a trapezoid.  We already know its two bases, so it remains to find the height.  In an isosceles trapezoid, the segment connecting the midpoints of the two bases is perpendicular to both bases.

8.28 The assumption that $CE$ is tangent to the circle gives too much away.

8.30 Draw a diagram, as precise as possible.  Use Power of a Point to get $AD^2 = BC\cdot BD$, and solve an equation.