Question

BC is tangent to circle A at B and to circle D at C. What is AD to the nearest tenth?

A. 21.6
B. 19.3
C. 18.1
D. 18.7

Answer 1

`Look\ at\ the\ picture.\\\\Use\ Pythagorean\ theorem:\\\\|AD|^2=2^2+18^2\\\\|AD|^2=4+324\\\\|AD|^2=328\\\\|AD|=√(328)\\\\\boxed\to\fbox{C.}`

Answer 2

(C) 18.1

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=√(328)`

⇒
`AD=18.1`

Therefore, the value of AD is 18.1.