Answer:
(C) 18.1
Step-by-step explanation:
Given: BC is tangent to circle A at B and to circle D at C.
Construction:Join DE such that DE=BC=18.
Solution: Since the radius of the circle A is BA=7 and the radius of the circle D is CD=5, then EA=7-5=2.
Now, from the ΔDEA, we have
[tex](AD)^{2}=(ED)^{2}+(AE)^{2}[/tex]
⇒[tex](AD)^{2}=(18)^{2}+(2)^{2}[/tex]
⇒[tex](AD)^{2}=324+4[/tex]
⇒[tex]AD=\sqrt{328}[/tex]
⇒[tex]AD=18.1[/tex]
Therefore, the value of AD is 18.1.
