Hello LUANDATO.
Let's take a look at your question.
As CD is perpendicular to AB then AD=DB. Let's name this lenght as "y".
So, the right triangles ADC and BDC has two sides of the same lenght, so BC=AC=5.
By the other hand, CO=r=25/8. Let's name OD as "x".
We need to find "y" to get the perimeter.
Using the Pythagoras theorem we have that: $$5^2=y^2+\left(\frac{25}{8}+x\right)^2\ \leftrightarrow\ 25=y^2+\frac{625}{64}+\frac{25}{4}x+x^2$$ and $$\left(\frac{25}{8}\right)^2=y^2+x^2\ \leftrightarrow\ y^2+x^2=\frac{625}{64}.$$ Replacing this last equation in the first one we have: $$25=\frac{625}{64}+\frac{625}{64}+\frac{25}{4}x\ \leftrightarrow\ 25=\frac{625}{32}+\frac{25}{4}x\ \leftrightarrow\ x=\frac{7}{8}.$$ Now, we can find the value of "y". $$y^2+\left(\frac{7}{8}\right)^2=\frac{625}{64}\ \leftrightarrow\ y^2=\frac{576}{64}\ \leftrightarrow\ y=3.$$ Now, the perimeter of the triangle is $$P=AC+AB+BC=5+2\cdot3+5=16.$$ So, the correct answer is C.
I hope this explanation can help you.
I'm available if you'd like a follow up.
Regards.
