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NOW I'm screwed!

 
 
Picture of David Tang
NOW I'm screwed!
by David Tang - Monday, November 11, 2019, 4:44 PM
 

Now, I need help on 24) and 30)!

 
Picture of Areteem Professor
Re: NOW I'm screwed!
by Areteem Professor - Tuesday, November 12, 2019, 3:39 PM
 

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 $DM$.