For both 8.5 and 8.10 a good place to start is using Power of a Point.

In case you were referring to 8.15 and 8.20: Recall if $ABCD$ is a cyclic quadrilateral, $\angle A +\angle C = \angle B + \angle D = 180^\circ$, and Ptolemy's Theorem says $AC\cdot BD = AB\cdot CD + AD\cdot BC$.

On 26.a try drawing triangles that make the regions $A$ and $B$ really really small. For 26b, you want to make $A$ and $B$ as big as you can (just remember that $C$ is the largest region), so what kind of triangle would you have in this case?