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
\((AD)^{2}=(ED)^{2}+(AE)^{2}\)
⇒\((AD)^{2}=(18)^{2}+(2)^{2}\)
⇒\((AD)^{2}=324+4\)
⇒\(AD=\sqrt{328}\)
⇒\(AD=18.1\)
Therefore, the value of AD is 18.1.
