In circle A as pictured above, segment DC is tangent to circle A at D.

Also, DC = 24 and BC = 18.

Find the length of the radius of circle A.

A)7

B) 6√7

C)25

D)12√5

In circle A as pictured above segment DC is tangent to circle A at D Also DC 24 and BC 18 Find the length of the radius of circle A A7 B 67 C25 D125 class=

Respuesta :

  • AC=2(BC)=2(18)=36
  • DC=34

Now

It's a right angle triangle

Perpendicular be radius and P

Apply Pythagorean theorem

[tex]\\ \rm\rightarrowtail P^2=36^2-24^2[/tex]

[tex]\\ \rm\rightarrowtail P^2=720[/tex]

[tex]\\ \rm\rightarrowtail P=\sqrt{720}[/tex]

[tex]\\ \rm\rightarrowtail P=\sqrt{2(2)(2)(2)(3)(3)(5)}[/tex]

[tex]\\ \rm\rightarrowtail P=4(3)\sqrt{5}[/tex]

[tex]\\ \rm\rightarrowtail P=12\sqrt{5}[/tex]

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