In the diagram, ab is tangent to c, ab = 4 inches, and ad = 2 inches. find the radius of the circle.

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

3 inches

y < -3

step-by-step explanation:

-3y - 2 > 7

-3y -2 + 2 > 7+2

-3y > 9

-3y/-3 < 9/-3   (change the inequality sign when multiplying or dividing by a negative number)

y < -3