Answer:
r = 15.2
Step-by-step explanation:
Where AB meets the circle creates a right angle. This is a right triangle problem involving missing sides. This means that we will use Pythagorean's theorem to find the length of the radius. Pythagorean's theorem applies this way:
[tex]10^2+r^2=(r+3)^2[/tex]
Foiling the right side gives us the equation:
[tex]100 + r^2=r^2+6r+9[/tex]
When we combine like terms, we find the squared terms cancel each other out, leaving us with
100 = 6r + 9 and
91 = 6r so
r = 15.2
