Question

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

Answer 1

A. 3 inches hope i helped please help with mine :D

Answer 2

Option A. 3 inches will be the answer.

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 =
`(12)/(4)`

r = 3

Therefore, Option A. 3 inches is the answer.