For 24 do first the case when the line is tangent, so $Y = Z$. Then do the case when $\overline{YZ}$ is a diameter of the circle. For the general case, consider points $Y'$ and $Z'$ so that $\overline{Y'Z'}$ goes through $X$ and $Y'Z'$ is a diameter. What can you say about quadrilateral $Y'YZZ'$?

For 30, use Power of a point to find the length of $CD$. Use this and the similar triangles $\triangle CDN \sim \triangle BDM$ to find the lengths of $BM$ and $DM$.