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Now, I got the first one by using the like triangles. This is my work, please tell me if I'm right: $\frac{t}{h}=\frac{x+t}{r}\Rightarrow x+t=\frac{rt}{h}\Rightarrow x=\frac{rt}{h-t}$ Now, I figure that $(b)$ must use the same concept (big triangle=little triangle). But I don't know what or how to do so. Please, give me general hints and only start me off, do not solve this problem for me.

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    Austin, both are correct. Sorry... Fell asleep"2012-08-10

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For (b), use similarity to conclude that $\frac{x}{t}=\frac{r}{w},$ where $w$ is the remaining side of the little triangle. There remains some work to do.

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    @AndréNicolas Thanks for the help. Your small comment actually helped a ton! How ironic.2012-08-10