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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

BC is tangent to circle A at B and to circle D at C What is AD to the nearest tenth A 216 B 193 C 181 D 187 class=

Respuesta :

dalendrk
[tex]Look\ at\ the\ picture.\\\\Use\ Pythagorean\ theorem:\\\\|AD|^2=2^2+18^2\\\\|AD|^2=4+324\\\\|AD|^2=328\\\\|AD|=\sqrt{328}\\\\\boxed{|AD|\approx18.1}\to\fbox{C.}[/tex]
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boffeemadrid

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.

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