Answer: AB is 12 units long
Explanation:
CD and BC are radii of the same circle. We are shown BC = 9, so CD is also 9
Through the segment addition postulate, we know that,
AC = AD + DC
AC = 6 + 9
AC = 15
The angle ABC is 90 degrees as this is a tangent point at the circle.
Triangle ABC is a right triangle. The leg AB is unknown, which we'll call x. The other leg is BC = 9. The hypotenuse is AC = 15
Use the pythagorean theorem to solve for x
a^2+b^2 = c^2
x^2+9^2 = 15^2
x^2+81 = 225
x^2 = 225-81 ... subtracting 81 from both sides
x^2 = 144
x = sqrt(144) ... applying square root to both sides
x = 12
AB = 12
