Answer:
Option A. 3 inches will be the answer.
Step-by-step explanation:
In the given diagram, line AB is the tangent to the circle C.
The given sides are AB = 4 inches,
AD = 2 inches
We have to find the radius BC of the circle.
By the theorem of tangents
If a tangent is drawn to a circle, radius of the circle will be perpendicular to the tangent at the point of tangency.
So by Pythagoras theorem in triangle ABC
Hypotenuse² = Base² + Height²
AC² = AB² + BC²
(AD+DC)² = AB² + BC²
(2 + r)² = 4² + r² [ r = radius of the circle]
4 + 4r + r² = 16 + r²
4 + 4r = 16
4r = 16 - 4
4r = 12
r = \(\frac{12}{4}\)
r = 3
Therefore, Option A. 3 inches is the answer.
