Answer:
A. 3 inches
Step-by-step explanation:
The radius BC and the tangent AB form a right angle, so triangle ABC is a right triangle. BC and CD are radii of the same circle, so they are congruent.
a^2 + b^2 = c^2
(BC)^2 + (AB)^2 = (CD + AD)^2
Let the radius BC = CD = x.
x^2 + 4^2 = (x + 2)^2
x^2 + 16 = x^2 + 4x + 4
16 = 4x + 4
12 = 4x
x = 3
Answer: 3 inches
