Question

cb is tangent to ⊙a at point c. find the radius.
cb ⊥ ac by the radius - tangent theorem, so ∠c is a right angle.
△abc is a right triangle, so apply the pythagorean theorem.
use the steps and solve for the radius.

1. $r^2 + 8^2=(r + 5)^2$
2. $r^2 + 64=r^2 + 10r + 25$

$r = $
39/10
54/25
64/35
89/10

Explanation:

Step1: Simplify the equation

We start with the equation \( r^2 + 64 = r^2 + 10r + 25 \). Subtract \( r^2 \) from both sides of the equation.
\( r^2 - r^2+ 64 = r^2 - r^2+ 10r + 25 \)
\( 64 = 10r + 25 \)

Step2: Solve for \( r \)

Subtract 25 from both sides:
\( 64 - 25 = 10r + 25 - 25 \)
\( 39 = 10r \)

Then divide both sides by 10:
\( r=\frac{39}{10} \)

Answer:

\(\frac{39}{10}\)