Answer: Option C
[tex]a^2=h^2+(b-r)^2[/tex]
Explanation:
In the triangle below:
If AC=b and AD=r, by the segment addition postulate:
[tex]\begin{gathered} AC=AD+DC \\ b=r+DC \\ \implies DC=b-r \end{gathered}[/tex]
Therefore, applying the Pythagorean theorem to the right triangle BDC:
[tex]a^2=h^2+(b-r)^2[/tex]
The first step to proving the Law of Cosines is Option C.
