In the diagram, line ab is tangent to circle c , ab = 4 inches, and ad = 2 inches. find the radius of the circle.
a. 3 inches
b. 2 inches
c. 5 inches
d. no solution

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 =

r = 3

Therefore, Option A. 3 inches is the answer.

d. vertex

step-by-step explanation: